Two numbers are in the ratio 2:3 and the difference of their squares is 320. find the numbers?

Two numbers, x and y related by the given ratio.

One equation:  x/y = 2/3

Formulate the second equation and proceed.

No!!!

let the nos. Be 2x and 3x.

9x^2 -- 4x^2 =320

or 5x^2=320

or x^2=64

or x=8

so, the numbers are 16 and 36.