I slept with my gf's best friend while she was in the other room?

three nights ago. nothing that i can say will ever justify what i did and i'm so ashamed that i wont have with my gf which is making her apprehensive. i suffer from depression and my gf always takes care of me no matter what and i've repaid her in such a shitty way. i'm not afraid of the consequences which it will have on me, i'm afraid of hurting her and i know it's too late to be thinking about the pain now, but i have to tell her, but how? should i just leave with no explanation - i can't get the feel of her friend off me and it makes me sick to think i allowed another waman that intimacy that for the past few years i've only had with my gf