He caught me cheating on him and didn't say anything

I Cheated On My Boyfriend With Another Guy,He Found Out And Didn’t Say Anything- What Should I Do?
2 months ago, I had a heated argument with my boyfriend and I left his place angrily and we did not communicate for about 2days as we were both mad at each other.
I had this guy that had always been on my neck, asking for a relationship with me and we got talking these two days. I was really mad at my boyfriend and I enjoyed the attention I was getting from the other guy.
I had s*x with the guy a few days after; 4days to be precise.
I never meant to cheat on him but I was angry and mad at him I thought I was going to break up with him after what happened but needed to find someone else so that it would be easier to break up with him.
After a week, we settled our quarrel and he found out I cheated on him from a text on my cell phone.
The truth is, deep in my heart, I love him so much and didn’t want to leave him. I was with the other guy only for a week and it was nothing special. That was when I realized I miss my boyfriend. I only did what I did, because I was mad at him.
When he saw the text on my phone, we were at a party with his friends, and he didn’t say anything, he acted so normal and didn’t want his friends knowing about the issue.
After we got back home, he didn’t call or text me for like 2days. It’s almost a month now and we haven’t seen since then.
He called me sometimes ago, telling me he wanted to travel out of time to spend some time at his aunt’s. He had never been close to his extended family and so I knew he was lying.
He texted me 7 days ago, which was my birthday, saying he missed me, and wished me a happy birthday. I was happy he remembered and then i knew that there’s still a way to get back to him. I texted him back and asked him if we could get back together and he told me that his friend has been seeing me around with a guy and I should forget about him.
He said after what happened, he was waiting for me to chase him and show him I was sorry for what happened, he said he told me he was leaving town to see my reaction but yet I did nothing. He said he loved me and we could still remain friends if I wanted, which I agreed to, hoping that was a step to getting him back.
Its 4 days now and nothing from him. I still love him. Is it still possible for me to win him back?