Question 1872
let the first interger be x and the second be y

we know 2 things...y-x=1 and {{{(x+y)^2 = 361}}}

sub the first equation, for y, in the second, to give {{{(x + (1+x))^2 = 361}}}. This becomes {{{(2x+1)^2 = 361}}}

Hence, taking a square root of both sides gives (2x+1) = +19 or -19

Therefore, 2x = 18 or -20 and then x=9 or -10.

Therefore the 2 integers are either (9 and 10) or (-9 and -10)

cheers
Jon.