Let the first even number be n+2. Then the next will be n+2.

It is given that one-third of the square of the larger one is two less than five times the smaller one.

Definitely (n+2) is the larger one.

`(n+2)^2/3 = 5n-2`

`(n+2)^2 = 3(5n-2)`

`n^2+4n+4 = 15n-6`

`n^2-11n+10 = 0`

`n^2-10n-n+10 = 0`

`n(n-10)-1(n-10) = 0`

`(n-10)(n-1) = 0`

n = 10 or n = 1

Since n is an even number n should be 10. So the next number will be 10+2 = 12.

So the two even numbers are 10 and 12.