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.

I found the numbers.

But you know what they say ... "Finders, keepers" ... So I'm keeping the numbers to myself.