Try to fix it or not?

I walked into the bathroom on my husband Facebook messaging a girl, 10 years younger than him, from his work at 4:30am (when I should be sleeping but woke up to pee). He real quick tried to close it out but when he closed the message her profile popped up because obviously to message her he had to click message on the profile. I lost it, completely broke down. I love my husband so dearly that this hurt bad. I mean heart shattering, crying all day pain. I’m so upset. I want to try to work it out but he is having a hard time committing to working it out because he says that he is so sad he broke us. He said he just has pain when he looks at me because he betrayed me and that he doesn’t see me the same anymore. He said he feels uncomfortable in the house like I should have kicked him out. He doesn’t feel like he should still be here. Please help me. Share your experience. Did you try after something like this and did it work. He told me it was only 3-4 days and there was nothing bad. He said flirty but told me the messages were all deleted because he was deleting as he went. I am just so hurt. I haven’t ate anything all day.