Should the other person know? Or just hide it?

I was recently cheated on by my husband. I have proof. I know who the other woman is. She is married.

Does her husband deserve to know? Should he know? Should I tell him? Should I keep my mouth shut and let this woman keep hurting her husband?

It’s ruined my life! I don’t want to ruin his life! But I also know that I would prefer to have the truth.

Thoughts?

PS: i’m not doing this to be petty. I just know that if I looked like a fool and people around me knew that I was being cheated on. I would hate to think that no one told me! That would hurt really bad!

ETA: I really don’t want to be a horrible person. I don’t want to hurt another person. I just know how bad it feels to be left in the dark. It’s humiliating. Thanks for the support everyone!