He was in fact, living and working over the continent in Europe, travelling from one place to the other, solving crimes and slowly breaking up Jim Moriarty's insiduous criminal web. It had taken him far longer than he expected, far longer than he would have wanted. Sherlock knew he couldn't risk returning to Baker Street until he had arrested or killed the top members of Moriarty's network. If any of them knew he was alive it was entirely possible, and likely, that they would try to exact some kind of revenge for their dead leader, targeting either Sherlock himself, or his friends. And there was no way he was going to put them in danger again.
It was a painstaking process, involving lots of undercover work, infiltration, spies, snitches, inside men, and as much information as possible fed through from his brother Mycroft, one of the few people who knew of his continual existence. It was interesting work though. Exciting, dangerous. And he was rarely bored. He rarely had time to stop and think, but when he did, his thoughts always turned to John. Sherlock missed John more than he could ever have imagined. He was glad of the constant work, the fighting, the violence, the crimes, anything, anything at all to stop him thinking about his only friend. The only person in the world who had ever trusted him. The only person in the world he had ever trusted, and he'd had to leave him behind. Occasionally he would dream about him, dream of them being together again, a team, an unbreakable unbeatable partnership. He only felt like half a detective without his trusty blogger.
Aside from the main part of his job tracking down agents, assassins and criminals working for Moriarty, Sherlock also helped out with minor crimes, murders and little mysteries in a similar way as he did in London. Working under the pseudonym of Sigerson he managed to build up quite a reputation in his own right. Throughout all of this, there was one man who continued to elude his grasp - a man named Sebastian Moran. Ex-army like John. A top sniper and at one time considered to be Moriarty's right hand man. Sherlock had heard rumours, reported sightings, had studied and learnt everything there was to know about him, but never actually met or seen the man himself. It was infuriating and annoying, but he continued to ask his spies and informers everywhere he went, telling them to keep their ears to the ground for any news.