The sum of two integers is 9 and the sum of their squares is 53?

integers are either 1 and 8, 2 and 7, 3 and 6 or 4 and 5

Squares are 1 + 63, 4 + 49, 9 + 36 and 16 + 25

Only 4 + 49 sums to 53 so your answer is 2 and 7