I am sorry you find yourself in this common sitch. I am glad you found this support group. It is full of great people with many different perspectives. The hard part for most is grasping the appropriate changes needed and applying them at the appropriate times. You will get conflicting advise. The key is to identify when to use specific advise.
For example, you will be told to act happy. There are times whens you should absolutely do this. There are other times when you should control all of your emotions and not react emotionally.
A couple of my mantras: "I am the emotional rock" and "The first one to react emotionally looses"
Obviously you are angry about your wife's behavior. It is your job to control this anger. You channel this anger into positive changes. Maybe in the past you yelled at her. Now you just listen. You can release this anger at a later time. Some guys lift weights. Releasing emotions is healthy. Best to do this in a safe private place. Some people cry in the shower, some will park in a remote parking lot and scream and yell. Find ways to let it out.
Now that the affair is out in the open, it will not be as much fun for them.
The best way to get her back is the set her free. Focus on your behavior. Learn new ways to interact.
I have seen many relationships turn around. The sooner you let go trying to control this, the sooner things will turn around.