Let us take the numbers to be XY and AB.

X*A = 15. So X and A have to be the factors of 15.

Factors of 15 are 1*15, and 3*5.

As this is a 2 digit number, X and Y have to 3 and 5, not necessarily in the same order.

Y*B = 28. So Y and B have to be the factors of 28.

Factors of 28 are 1*28, 2*14, and 4*7.

Again as this is a 2 digit number, Y and B have to be 4 and 7, not necessarily in the same order.

Now the numbers possible are :

34 and 57 or 37 and 54.

Clearly 37*54 is not equal to 1938. But 34*57 = 1938.

So, the answer is 34 and 57.