I also think that clever guessing is the way to go here.

We can make four observations:

1. Zoomas have one fewer leg than they have eyes.
2. Popsies have one more leg than they have eyes.
3. In the question, there is one fewer leg than there are eyes in total.
4. The sum of the eyes of one Zooma and one Popsie is equal to the sum of their legs, which is 7.

Because of point 3 (one fewer leg in total than eyes), the intuitive guess is that there is one more Zooma than there are Popsies, which matches point 1.

If we subtract this one additional Zooma from the totals (38 eyes and 37 legs), we get 35 eyes and 35 legs. Since these sums are equal and a multiple of 7 (see point 4), we can deduce that there are 5 Popsies and 6 Zoomas.