I feel for you OP. As someone who was cheated on I know the pain you are going through. I know how difficult it is to get through every day and to try and keep a routine for the kids. My dd was 10 when her dad's cheating blew up in his face when I caught him.
But I was also a teen when my dad spoke to me one day out of the blue and told me he was leaving my mum. I was so shocked. He said there was no one else but of course there was. After that day I never saw or heard a thing from him for 5 weeks and had to watch my mum crumble. It affected me badly at school.
My only advice would be not to keep things from your kids, especially the eldest. You can say he has left for another woman as that is the truth. As a teen I would have handled things much better if I had known the truth early on.
It is his job to speak to his kids about his new life and his relationship with his kids moving forwards. You can reassure them he still loves them but be honest about the facts.
Just look after yourself try and drink and eat a little. I lost a lot of weigh too and had to have weeks off work. Just focus on you getting through one day at a time and keeping the kids routine, that's what gives them their feeling of safety.
I'm 2 years on my dd does not want to see her dad. I respect her decision now but hope she will have a relationship with him in the future. As a teen I didn't want a relationship with my dad either after it happened but years later it did improve.
He alone is responsible for his actions and his relationship with his kids. Don't excuse it to them but you can say that you hope he speaks to them soon and they can write to him with letters to a family members address possibly