I think that your e-mail indicates that she slept with someone else while the two of you were broken up. If that’s true, then she didn’t really cheat on you. However, if you can’t get over the fact that she did sleep with someone else regardless of the fact that it was while the two of you were broken up, then you’ll never be able to trust her. If you can’t trust her, there’s not much place for a relationship since trust is paramount in any relationship.
Remember that everyone brings baggage to a relationship. Sometimes it’s the number of ex-boyfriends or ex-girlfriends you may have or a difficult family or illness or job demands. Understanding that baggage is part of everyone and no relationship escapes both parties’ baggage, it may help you let go of the fact that she slept with someone while the two of you were not a couple.