So sorry. You must feel as though you have been hit by a truck. There is no feeling like it.
You said that there was "no discussion" and if that means that you are still in the dark about the details of the affair, then I'm afraid this is a typically cowardly response from someone who wanted to get the message out, but didn't have the balls to give you some understanding.
All the advice about how to cope with the acute nature of this crisis is absolutely sound, but I suspect you will need a lot more information from him to piece together how your world came to crash down without warning. He owes you this much.
I would echo the advice about being dignified but cold with him, but I do think you need some information. Therefore I would insist that he spends some time with you telling you his version of events. I will warn you that a lot of this will be delusions, re-writing of history (to justify what he has been doing) and outright lies, but try to focus on indisputable facts, such as when it started, who knows, when and how often they met etc.
The reason I am suggesting all this to you is in case you are like me and need to make sense of the last 2 years. It really helped me to timeline everything and it sort of gives you back your power when you start to fit the jigsaw pieces together. Things like when he perhaps said he was stressed, or didn't want to attend an event with you....with your new knowledge, you can rewrite these things for yourself, this time with the truth.
One of the things I often recommend too in a shock situation is to spend some time analysing when you last felt truly happy. This question often allows us to pinpoint more accurately when affairs started - and allows us to see that the stories some betrayers weave about being unhappy first and in consequence had an affair, are nonsense. More often than not, the affair started and this led to dissatisfaction in the marriage.
I must also echo the advice not to beg or plead. Contempt would be good, but coldness will do. He must be under no illusions that he has lost everything. Ask your parents though to give you some space to talk.
Take any mothering and pampering you can get at the moment, because you are in shock. You will feel disbelief that the world is still turning and that other people are getting on with their everyday lives. Regard any help as help to your DCs, because they will need you to be strong and fit.
Do keep posting.