can you beat einstein's second attack

[CPL.Luke]

http://en.wikipedia.org/wiki/Bohr_Einstein_debate#The_principle_of_indeterminacy_applied_to_time_and_energy

 

 

during the einstein bohr debates einstein proposed a very precise way of determining the amount of energy radiated in some very precise interval (detailed in the above link). originally stumped bohr later found a solution that showed that the error in the experiment corresponded exactly to the indeterminacy relation between time and energy.

 

my question is if anyone here knows how to solve it out mathmatically as it seems like this would be a very cool derivation. (or if someone can find it layed out somewhere)