My guess would be that if he was on a one-way contra-flow then he is mostly responsible. He should have come out the correct way and he clearly didn't follow the regulations.

Go into your local police station and tell them what happened, show them your photos and ask their advice. One thing to remember...your insurance company will not want you to claim responsibility and it is their obligation to fight your case so they win for you. Do not, under any circumstances, admit responsibility at all, either to the driver of the other car or your insurance company. Claiming liability will likely put you in a position of defense, rather than attack. Maintain your story and stick to the driving rules that the other driver should have been obeying.

Your insurance company will then fight for you and the worst scenario is a 'knock for knock' situation where they will hold neither driver responsible in full. Tell the police how it happened, where it happened and show them the pictures. They should be able to tell you.

Good luck.