algebra

integers are (x) and (x+2)

$x^2 + (x+2)^2 = 650$

$2x^2 +4x + 4 = 650$

$x^2 + 2x - 323 = 0$

$(x+19)(x-17) = 0$

The integers are positive, so x = 17.

The numbers are 17 and 19.

x ^2     +   (x-2)^2 = 650

x ^2 + x^2 -4x+4 = 650

2 x^2 -4x - 646 = 0

x = 19     x-2 =17