Given That The Product Of Two Numbers AB And CD Is A Three Digit Number EEE, Where A, B, C, D And E Are Distinct Non Zero Digits. What Is The Sum Of All The Possible Values Of AB?

Any number EEE will be the product of a single digit (E) and 111. 111 = 3*37, so factors of EEE are 37 and 3*E.
We know that the value of 3*E must be a two digit number, so E >
3.

We already have one factor (AB or CD) = 37, so the possible values for E are 4, 5, 6, 8, 9.
E will not be 9, because 3*9 = 27, which contains a 7, a digit that is already used.
E will not be 5, because 5 must be the least significant digit of a factor, and 5 cannot be used twice.
This would seem to leave 4 possible products.
  12*37 = 444
  18*37 = 666
  24*37 =12*74 = 888
Possible values of AB are 12, 18, 24, 37, and 74. Their sum is 165.