It's not going to be easy but you will get through this.
Go see a lawyer before you do anything else. Usually the ex will tell you not to see one but you must see one even if it's just the one visity they will let you know where you stand.
I am in a similar situation 21 years of marriage and 4 children. I found out my husband was seeing someone and he left that day as well. It has been extremely hard. I did meet with a lawyer however things are somewhat at a standard right now. Everyday I feel like my emotions are all over the place, I go from angry to very sad. I wish you the best and hope you and your children get through this situation the best way possible.
Definitely consult a lawyer now. I also highly highly recommend "20 Years Gone: A Divorce Story" by Dorian Wright (available on Amazon), as you will find many tips and details to use in your current situation.
I would also recommend looking to see if adultery is recognized in your state for reason for divorce. As unreal as it may seem, some states do not recognize it.