Both EU negotiator Michel Barnier and his United Kingdom counterpart David Davis said they were heartened by the first day of talks on Monday and insisted the tight deadlines were tough but achievable.
In carefully choreographed talks that even saw the two men exchange mountaineering gifts, they agreed to discuss divorce issues before negotiations on a future trade deal can start.
"N. Ireland has taken more time today than anything else", said Davis on UK's behalf reminding that the issue is politically sensitive, just to add that determining an invisible border is the point.
David denied any retreat by his government, noting that "both sets of dialogue will continue once the European Union 27 will agree that divorce talks have reached "sufficient progress".
Mr Barnier said they must ensure Brexit proceeds in an orderly manner.
"I would like us to get a good agreement that is in both sides' interests".
Britain now appears to have given in on the EU's insistence that the negotiations first focus on three key divorce issues, before moving on to the future EU-UK relationship and a possible trade deal.
A top German business lobby is urging negotiators for Britain and the European Union to quickly come to an agreement over how Britain's departure from the EU will affect cross-border trade - and avoid a "hard Brexit".
The Brexit secretary David Davis had previously rejected this and predicted that it would be the "row of the summer" once negotiations began.
Britain's Department of State for Exiting the European Union tweeted a picture of a smiling Davis and a straight-faced Barnier "after exchanging mountaineering gifts,".
"They should be agreed alongside each other, this is completely consistent with the Council's guidelines which state nothing is agreed until everything is agreed". Davis also said the United Kingdom plans to set out its own negotiating aims for Brexit next Monday.
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Davis, noting shared security threats for governments across Europe hours after a van rammed worshippers at a London mosque, said: "There is more that unites us than divides us". "It's not about punishment, it's not about revenge".
The first formal negotiations took place just short of a year after British voters narrowly chose to leave the European Union, which was long a source of love-hate angst in British politics. He said that the other European Union countries have a united position but the British are "in chaos".
He also confirmed that Britain would opt for a "hard Brexit" that involves quitting the EU's single market and customs union, rejecting suggestions that after a poor election performance by May the line might be softened.
"And the consequences are substantial".
"The pessimist see difficulty in every opportunity, the optimist sees opportunity in every difficulty".
But many in Brussels fear that London has no real strategy, with May under pressure at home and still trying to close a deal with a conservative Northern Ireland party to stay in power, and facing criticism for her handling of the aftermath of a devastating tower block fire.
The two sides are expected to meet monthly until March 2019, when Brexit is due to happen.
In addition to the working groups, a "dialogue" has been established to deal with the Irish border issue, under the authority of Barnier and Davis' right hands, Sabine Weyand and Olly Robbins.
Officials on both sides play down expectations for what can be achieved in one day.
"Where possible, both parties will seek to agree public statements relating to negotiating rounds", the document stated.
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