It will, or it does?

Based on the logic and flow, it will:

Ask for the input
Ask for numbers based on the entry as long as it isn't an 'e'
Print the output
Ask for an input again

If the initial input is 'e', it will skip the while statement altogether and exit
If the input is 'e' after the initial input, it will exit the while because the condition is now false and exit

I see it working just fine. You might have to work you \n's here and there to add the proper line breaks, but that's all...