since there are not many numbers, let's try and do this by trial and error

here are the pairs of integers who's sum give 15

1 + 14 ...........1^2 + 14^2 = 197

2 + 13 ...........2^2 + 13^2 = 173

3 + 12 ...........3^2 + 12^2 = 153

4 + 11 ...........4^2 + 11^2 = 137

5 + 10 ...........5^2 + 10^2 = 125

6 + 9 ............6^2 + 9^2 = 117

7 + 8 ............7^2 + 8^2 = 115 ........this is your guy

and they repeat with the second number taking the place of the first and the first taking the place of the second

i'm sure TPH or someone else can come up with a neater way to do this