Oh, OP. I am so sorry. This is just a horrible discovery.
I'm not sure I'd believe the part about it only being a happy ending. Why would he pay for that only?
So, basically, it seems to me that some people cannot live up to the vow of fidelity in marriage for decades on end. The question is, what are you going to do about it? Can you try to get to the bottom of WHY he did it? Do you have a good sex life but he wanted some variety? This is bad, because it's not something you have the power to fix. Or is your sex life spotty/boring/infrequent/non-existent, and he began to feel he couldn't live the rest of his life like that? Still really bad - he should have talked to you - but something you could potentially work on together.
I really do not know how I feel about sexual fidelity in longterm marriages. I'm the endlessly faithful type, but I know that a lot of people eventually struggle with it, even if they're not normally the playing-around type. If it happened to me, on the one hand it seems crazy to throw away all your memories and years and your future because of some brief physical interaction. On the other hand, it's a heartbreaking betrayal and could be hard to move on from, I imagine.
My head thinks that we place far too much emphasis on the physical, if he made a mistake and doesn't love the other woman. But I would have no idea how to make my heart agree with that.
OP, it depends what you want, moving forward. Some people cannot get over physical infidelity, and that's OK. Some people don't think it's the most important aspect of a relationship and that their shared interests/sense of humour/history/kids/life together are more important than a physical betrayal.
I heard a good piece of advice once. It said that when you have to make a difficult decision, make one that you can live with over time. Do you think that twenty years from now you would regret breaking up over this? Or can you picture yourself happy in a new life without him, be that single, dating, or remarried?
Only you know how you feel. I am extremely sorry you're going through this. I honestly do not know what I'd do in your shoes. I'm a big romantic, so it would probably kill my love for him. Some people are more practical and less emotional about physical betrayal. It's your call.
Sending you big hugs xxx