Make sure he doesn't have any issues (bed wetting, fear of being laughed at for sleeping with a blankie or toy, night terrors, etc.) My youngest daughter has a nervous stomach and feels sick when she goes on a long trip away from home or to sleep over most places. Maybe he feels that way. I started really pushing my daughter to stay with her cousin or her best friend when she was eight or nine, and she's been away to retreat weekends and then to week long camps. Generally she's unhappy the first day or two of a week long camp but then is fine. She does much better on a long weekend. Her problem with her nervous stomach is that she needs some private bathroom time, and with camp schedules the way they are she doesn't always get it. When she does, she's okay and has a great time. But i had to push her to do it, she'd have never gone on her own.
But three days isn't very long even if he's unhappy. His friends will be there, so he'll have fun at least part of the time. If it's really terrible, they'll call you. He's old enough to understand that you're not abandoning him and that you'll come back for him soon, his friends are there and he's going to want to be cool in front of them, and he can understand that if he really, really can't take it, he can come home, but that he should try to be really brave and stick it out at least one night, and then if it doesn't get better he can rethink it. If he's just worried about being away from you, I think he'll be okay after the first night. If the older boy makes it all three days and has fun, the younger one will be happier about doing it next year or the year after.
I don't think he'll be very unhappy. He may be anxious and he may not sleep well, but he'd get through it and be proud of himself for sticking it out. You could give him something very small, like maybe a stone with a word carved on it (you can get them at Christian stores with inspirational words) like Faith, and tell him he can hold it while he sleeps and that it will remind him to have faith that Mommy and Daddy know he'll be fine and are available if needed, and that God is watching him at camp just like he does at home. That gives him a reminder of your love and something to touch when he's anxious without being babyish like a blankie.
Of course, the eight year old will not be happy sleeping alone, either, but it's a good time for him to learn to do it, too. They're old enough to understand what's going on and to learn to handle their emotional reactions. You could have the ten year old ask his little brother to take care of something belonging to him while he's away.
Remember that if he really, really hates it, you can always go and get him, but you should encourage him to stay. My daughter called from Girl Scout camp at bed time crying and wanting to come home. After talking to her for a few minutes, I got her leader on the phone and asked if she could take her to the main building and let her use the indoor bathroom alone for a few minutes. She called back later and said she was fine and was staying and she had a great time. So sometimes you just have to figure out why they are uncomfortable and solve their problem. You have to pull it out of them, they don't always know what the problem is themselves. But if you can figure that out, you'll have given them freedom from that fear, and that's a wonderful thing.