It's a little awkward, because you'd need to parse the strings in reverse, but if all you need to do is sum, you can do it one digit at a time, while at any given moment only handling only one character from each input string, a carry byte, and one output character.
How do you know where the first string ends and the second starts? Did you miss the "stdin" part?
This is not
./program first_number second_number
You don't need to parse the strings in reverse. That's for printing integers, not parsing. Roughly: