Let's give our numbers names: we'll call the number of bowls of tomato soup t and the number of bowls of chicken soup c.
We know from the question that c is 4 less than t, so we can write that fact as the equation
c = t - 4
We <em>also</em> know that, when we add both of the amounts together, we get 10, so that
c + t = 10
We can then use the first equation to replace c with t - 4:
(t - 4) + t = 10
or, rearranging:
2t - 4 = 10
This means that if we <em>double the number of tomato bowls and subtract 4, we arrive at 10</em>. To find what exactly t is, then, we can go the other way around. If we <em>add </em>4, we see that 2t = 14, and if we <em>halve </em>2t, we find that t = 7, so the cafeteria sold 7 bowls of tomato soup.
Checking our work, we see that c = 7 - 4 = 3, and 7 + 3 = 10, so this answer is consistent with what we've been given.