#### Answer

$33, 50$

#### Work Step by Step

let's call the two numbers $x, y$
We know that:
$x + y = 83$
and
$x - y = 17$
By the first equation
$x + y = 83$
$x + y - y = 83 - y$
$x = 83 - y$
let's use the second equation and switch $x$ for $83-y$
$x - y = 17$
$83-y - y = 17$
$-2y + 83 = 17$
$-2y + 83 - 83= 17 - 83$
$-2y = -66$
$-2y \times \frac{-1}{2} = -66\times \frac{-1}{2}$
$y = 33$
Therefore
$x = 83 - y = 83 - 33 = 50$