To be completely honest both of those sound a little strange because when you say the earliest by itself it isn't enough to transmit a complete thought in this context 
but if I had to pick one I'd understand better it would be the second one 
There are many ways to say something like that for example
1. I am awaiting your response I need it as soon as possible  (more forceful) 
2. I'm am looking forward to hearing from you as soon as possible. (More polite)