interpetation is crucial:

x(x+1) = x + (x+1) + 89

x^2 + x = 2x + 90

x^2 - x - 90 = 0

(x-10)(x+9) = 0

x = -9 or 10

10 is the root to use => the two numbers are 10 and 11

Okay so lets call the product =  x*(x + 1)

The sum would be =  x + (x +1)

This is what they tell us: x*( x + 1 ) = 89 + x + (x + 1)

From there on, we have: x^2 + x = 89 + 2x + 1

Put everything on one side: x^2 - x  - 90 = 0

Factoring, we have: (x - 10)*(x + 9) = 0

If we use x = 10, then numbers are 10 and 11

Or if we use x = -9, then numbers are -9 and -8.

11*10=110

11+10=21

110-21=89