This sounds an awful lot like a homework problem, so I'm not giving code. Just think about what you need to do. You are saying that you need to take the first character off the front of two strings, parse them to ints, and add them together. Finally, take the result of the addition and append them to the end of a new string. If you write code that follows that path, it should work out fine.
EDIT: As Ralph pointed out, you'll also need to check for overflows. I didn't notice that when I started typing. Although, that shouldn't be too hard, since you're starting with a two one digit numbers. If the number is greater than 9, then you can just subtract 10 to bring it down to the proper one digit number.