Are there more engineers than salespeople working at Soho Corp?

I would like to propose a mathematical way of solving this question. Though I seriously feel that mathematically, it would take more time to solve.
We can clearly notice that neither Statement 1 nor Statement 2 is individually correct.
Now we have to check if both the statement together can get us the answer.

From Statement 2, we have E+3 = 2S
From Statement 1, we have C=2/3(E+S)

Therefore, E+S+C=T (using T as the symbol for total)
After substituting the value of C from statement 1, and the value of E in the form of S from statement 2; we get,
E=(2T-5)/5
S=(T+5)/5
Now,
We have to compare which one is higher, E or S.
The values of E and S are clearly dependant on T. If we look at E and S a little closely, then we can surely say that for E to be greater than S, T must be greater than 5. We do not have any constraint on the value of T.

So let us say, if T=5, we get E=1, S=2, C=2. All conditions are satisfied. E<S
But if T=10, we get E=3, S=3, C=4. All conditions are satisfied. E=S
And if T=15, we get E=5, S=4, C=11. All conditions are satisfied. E>S.

Hence, both Statement 1 and Statement 2 together are not getting us the uniform answer.