MY (35M) GF (32F) HAS BEEN SENDING NUDES TO HER MARRIED COWORKER.

My (35M )girlfriend (32F)went out tonite with her sisters and friends for a bday dinner and she came home absolutely drunk I have never seen so drunk before , long story short she went to bed and her friends kept calling her to make sure she was ok. Her phone was opened to a work email, and that where I noticed her and her coworker were sending eachother nudes and talking through email for the past two years . I open her work email, thousands of messages going back 2 years , pictures , videos , her coworker is also a 45 year old married man .I confronted her about it and she is crying hysterically saying that nothing physical has ever happened between them , but their are messages saying meet me in the back hallway or meet me in the garage. I don’t know what to believe , she’s saying she didn’t cheat and that she will quit , that it was just foreplay / email sex or whatever .she also lives with me so that kind of sucks , will probably be a process to kick her out .not sure if I want to continue the relationship after this .what is the best way to go about this?