We have both addmitted to cheating. Can we work it out?

How everyone, this is the first time I post in a forum of any kind but I need help. Last few days have been a rollercoaster of emotion because in the same day my partner I have both admitted infidelity.

Myself and my partner love each other more than anything, I know that. We were going to move in together in September, already planning and getting excited about everything. It wasn't always like that. When we first started dating I was still into someone else and I boke it off after 4 weeks on that basis because I didn't want to lie to him. I was confused what to do. For about a month we kept in touch and I realised the other guy is a a$$whole and and I want to be with my current partner. Since then our love has blossomed tremendously.

Two days ago at a stag and he was drunk and he kissed someone. He also says that he pulled back once he realised what he's doing. He told me the next day and I got extremely upset. I decided I want us to stay together and it also prompted me to share my own secret. I told him that during those initial 4 weeks when I was in a confused state I slept with my best friend (girl) and he flipped. We've had endless arguments about whose it worse. I say his happened at the hight of our love and it makes me doubt he will never do it again. He's hurt because mine is more sexual and I hid it from him for a year. I am also hurt because he knows how much I need him right now and his betrayal comes at a bad time - few months ago I had an abortion. Since then I struggle because to some extend I blame him. So I see a betrayal from someone who now says he loves me more than the world and for whom I've made such sacrifices. He is hurt by my dishonesty because I hadn't told you for a whole year and it was sex.

We have both done something wrong and terrible and hurt each other. We've eroded each other's trusts. What are your takes on this? Can a relationship recover from this? What can we do to fix this?

Thank you all!