Question 261679
Let x = the first integer and
let y = the second integer

The numbers are consecutive, which gives us Eqn 1: y = x+1

Their product is -4 more than the square of the smaller one (x).

This gives us Eqn. 2: {{{xy - 4 = x^2}}}

We will now insert y = x+1 from Eqn. 1 into Eqn. 2:

{{{xy - 4 = x^2}}}
{{{x(x+1) - 4 = x^2}}}
{{{x^2+x - 4 = x^2}}}

Move everything to the left side and collect like terms:

{{{x^2 - x^2 + x - 4 = 0 }}}
{{{x - 4 = 0 }}}
{{{x = 4}}}

Which means that y = 5.

The two numbers are 4 and 5.