Answer
19 and 20
Work Step by Step
let's call the first number $x$, and the second will be $x+1$
We know that
$x(x+1) = 380$
$x^2 + x - 380 = 0$
$x^2 + 20 x - 19x - 380 = 0$
$x(x+20) - 19 (x + 20) = 0$
$(x-19)(x+20) = 0$
And because we know x should be a positive integer.
$x = 19, x \ne -20$
