Given that the concatenation ABCDE digits is a 9-digit zero-less pandigital number
and so is the sum S - there is only one sum S to make the above equation true.

Find it.

I was about to post similar remark, but after reading DM's remarks decided to address a basic issue:

Do elegance of the program and the runtime come into consideration prior to writing the final version of the program?

I have noticed that on several occasions  Charlie, who is in my eyes the ultimate programmer, introduced reasonable constraints regarding the approach and the quantity.