The best way to get through this is to shut the door on him and get on with your life. Don't contact him. Don't ask after him. If he leaves a message or sends a mail, ignore it. If it is something that can't be ignored, short factual replies, such as you'd send to your boss at work.
Keep busy. Are you working? If yes, focus, volunteer for any opportunities going, maybe work towards a promotion. Your dcs are adults, this is time for you to focus on you. If you aren't working brush up your CV, look for paid or voluntary work to get your skills up to date.
Do some things just for you. Join a gym/art class/reading group/walking group/other interest of your choice. Even if you are shy getting out there will feel good and will take your mind of things at home.
Lawyer up. Ask around for recommendations. Take copies of all financial documents and read them so that you understand your financial position. You can't use anything in your DH's name in court but you can catch him out if he lies.
I know all this seems daunting and final, but ironically if you did (inexplicably) want him back it's also the best way of giving him a short sharp reality check into what he is giving up. Right now he thinks he has all options open. He needs to see YOU are calling the shots now.
Lastly, even if he does come crawling home be very careful about taking him back. Read up on infidelity. It's very hard to recover from it, and recovery takes years. Years of feeling like you do now. It really isn't worth it.