#### Answer

$7,9$

#### Work Step by Step

Lets call the first integer x, and the second x + 2
$x(x+2) = 63$
$x^2 + 2x = 63$
$x^2 + 2x -63= 0$
$(x-7)(x+9) = 0$
$x = -9, 7$
The correct solution is 7, because -9 is not an integer.
Therefore the numbers are $7,9$.