Question 42404
Call the numbers x and x+1.
Thus we have
x^2 + (x+1)^2 = 85
x^2 + x^2 + 2x + 1 = 85
2x^2 + 2x - 84 = 0
x^2 + x - 42 = 0
(x + 7)(x - 6) = 0
x = -7 or x = 6
but you want positive, so your numbers are
6 and 7