I Messed Up

I feel sick to my stomach writing this. I cheated on my wife, Sarah. It was a drunken mistake at a conference. One stupid night with a coworker. It meant nothing, but it still happened. I haven't told her. I don't know if I can. The guilt is eating me alive. Every time I look at her, I feel like the worst person in the world. She trusts me completely. I hate myself for breaking that trust. I don't deserve her. I'm terrified of losing her, but I also know she deserves to know the truth. I just don't know how to tell her without destroying everything we've built. What do I do?