#### Answer

$11,13$

#### Work Step by Step

Lets call the first integer x, and the second x + 2.
$x(x+2) = 143$
$x^2 + 2x = 143$
$x^2 + 2x -143= 0$
$(x-11)(x+13) = 0$
$x = --13, 11$
The correct solution is 11, because -13 is not an integer.
Therefore the numbers are $11,13$.