The minute the email arrived on a quiet Friday at the end of August, those around Micheál Martin believed its contents were never meant to be confidential.

Brian Murphy, Leo Varadkar's chief of staff, had sent Deirdre Gillane, Martin's chef de cabinet, a text notifying her that she had mail.

In Gillane's inbox was a four-page letter – with an appendix across a further six pages – in which Varadkar outlined his party's performance in government to date, and argued for immediate talks on extending the confidence-and-supply agreement, which sees Fianna Fáil underpin the Fine Gael led-minority Government.

The following Tuesday, the entire letter was tweeted by Varadkar, angering Martin and those around him.

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“He [Martin] went mad over it,” said a Fianna Fáil frontbencher. “He felt it was a breach of the agreement, the agreement he had bent over backwards to maintain.”

The exchange over the letter typified the weaknesses both parties claim they see in each other’s leaders.

For Fine Gael, it proved yet again that Martin is prickly, thin-skinned and simply refuses to accept political communication has moved on; another confirmation that Varadkar is of the moment and Martin of the past. While the Fianna Fáil leader had the measure of Enda Kenny, he had yet to figure out the new Taoiseach.

For Fianna Fáil, it showed that Varadkar is obsessed with spin, can be shallow, lacks substance and is predominantly interested in playing games.

Martin rebuffed Varadkar, and said that a review of the deal – with Fine Gael eager to renegotiate an extension – could start only after the third and final budget of the arrangement. That review began this week.

“This battle is about the war, and the war is the general election,” said a senior Fianna Fáil TD, an assessment shared by a Fine Gael Cabinet Minister: “This is about sparring with each other for the next election.”

The Varadkar-Martin rivalry will be one of the defining elements of that election, and despite their uneasy relationship, those close to both men insist they share no personal animus.

A mutual respect arose after both brought the country back from the brink of a general election late last year over controversies involving Garda whistleblower Maurice McCabe. Although Frances Fitzgerald was eventually forced to resign as tánaiste, Varadkar told colleagues he felt Martin was genuine in trying to avoid an election.

“You got a sense off Leo that he felt that he [Martin] wanted to make sure that it didn’t come to an election, or that there wasn’t a breakdown in the relationship,” said a senior Minister. Martin is said to hold the same view of Varadkar’s approach at that time.

Communications between their two offices improved significantly after that, and Fianna Fáil anger over Varadkar’s August letter was, in part, due to a feeling that it was against the spirit that had prevailed last November.

Their private exchanges are more civil than their public differences might suggest. Each has an understanding of the other’s position – both are somewhat trapped by confidence and supply – yet struggle to reconcile such private civility with actions and insults when competitive politics resumes.

When Varadkar and Martin look across the Dáil chamber, they each see Dr Jekyll and Mr Hyde staring back.

Both admire the ruthlessness of the other, and hold a genuine respect for a serious opponent. Varadkar sees a survivor who is willing to bide his time to take his opportunities; Martin someone who clinically worked his way to the top.

Nor does the Taoiseach, according to sources, see the fight between himself and Martin in personal terms, but rather “in terms of two political parties”.

“Leo might accept his [Martin’s] bona fides more quickly than others, which might worry some people,” said a source. “You’d nearly tell him after meetings: ‘He’s the f**king enemy’.”

But their differences are most evident in the heat of Dáil debate. Martin is known to have found Varadkar, with the wind at his back, too eager to traduce his opponents, particularly his former cabinet colleagues on the Labour benches; an approach Fianna Fáil decries as college-style politics.

In turn, Varadkar feels Martin often feigns anger and makes accusations of dishonesty – and attacks on character rather than policy – too easily.

Sources say the Taoiseach believes Martin genuinely dislikes him, but that this should not be an impediment to the pair working together in government in future.

Varadkar doesn’t really “trust” Fianna Fáil, said a Minister, adding he is aware they may “delay and stall” the current talks only to cause an election in the new year after a winter of trolley and homelessness crises.

With that in mind, his Fine Gael negotiators will try to keep alive the prospect of a run to the country later this year, if a Brexit withdrawal agreement is reached.

Others say there is awareness at the top of Fine Gael that Fianna Fáil needs the political space to agree an extension to confidence and supply.

“If we can help them get to the point of a 2020 election, then why wouldn’t we?” asked a source close to Varadkar.

But, the source added of Martin: “We don’t have the fear he has.” From the Fine Gael perspective, Martin fears an election, unrest in his party and the threat that his TDs will remove him after an unsuccessful general election.

Not so, says a Fianna Fáil frontbencher. “He is not afraid of an election. He is confident about an election.”

With Fianna Fáil behind in polls, Martin knows there is interest among the public in Varadkar but believes support for Fine Gael, as a party, will not necessarily follow.

“He knows there is a difference between an interest in Leo, as opposed to an interest in Fine Gael,” a TD said. “That is why he is not getting spooked by opinion polls.”

It is his “genuinely held view” – informed by his own experience in government – that Fine Gael and Varadkar are obsessed by spin and have not produced anything of substance.

“Micheál thinks he has a very strong record in health and he looks at Leo and thinks: ‘What has he done in health?’ He doesn’t like his politics, he sees him as right wing, for the haves.”

Against that, a Fine Gael source draws comparisons between Martin and former leaders of the British Labour Party and the Tories who rebuilt their parties, but never made it to the highest political office themselves.

"He has brought Fianna Fáil back, but a bit like Neil Kinnock or Michael Howard, he ain't Tony Blair or David Cameron. Moses not Aaron."

Martin trusts very few in his own party, and nobody – aside from Gillane and perhaps a select few others – knows what his desired result from this round of confidence-and-supply negotiation is.

Some TDs intuit that he means to extend the deal, and those who engage with him every day believe he has an idea of what he wants to do, even if events could derail his plan.

“He absolutely has a road map in his head,” said a TD.

Another added: “Micheál and Deirdre seem to have decided that the longer he [Varadkar] is exposed, people will see he is a lightweight.”

After years of battling his own party – on issues such as standing presidential candidates, to the position many TDs took on abortion – as much as his opponents in the Dáil, the Fianna Fáil leader is more assured in his own judgment, having correctly called all the big political decisions of recent years.

At a recent frontbench meeting, he asked that people “trust” his approach to the confidence-and-supply talks. He also told some TDs who said the Fianna Fáil rank and file are still uncomfortable with confidence and supply to listen to voters in the wider electorate as well as party members.

A successful few weeks – from an appearance on The Late Late Show, to his offer not to collapse the Government until a Brexit deal is ratified – has cheered his parliamentary party, who echo his attacks on Varadkar.

In a testy exchange between the pair in the Dáil this week, Varadkar said Martin and Fianna Fáil cannot attack the Government on substance, so has to choose a different line.

“It is the obvious playbook for a party in a confidence-and-supply deal,” said one Minister of Martin’s jibes. “Those are the lines you take.”

In Fine Gael, it is also seen as a way of undermining Varadkar’s reputation as a straight talker by casting him as inauthentic. Party figures also disagree with the view that, in the final run-in, the narrative of the next election could be about who the voters want as taoiseach: Leo, or Micheál?

“I don’t think it is going to be a Fianna Fáil-Fine Gael contest,” one said. “If it is presidential contest, we’ll blow them away. If it is a team contest, we’ll blow them away. There is a better officer corps behind us.”

But a presidential contest could suit both Fianna Fáil and Fine Gael by squeezing smaller parties and Independents to the margins of the election debate.

The fighting elephants of Varadkar and Martin, Fianna Fáil and Fine Gael, could trample upon all else.

The confidence-and-supply talks will be a flavour of the coming brawl.