Is there a rule in English regarding when to use the word "energy" and when to use "power"?

For example:


  
  I don't have the energy to deal with the problem now.
  It takes a lot of brain power to understand the problem.
  



Question: How was this photo taken
Answer: This is mostly guess-work:

To me this looks like a medium length zoom:


(Assuming its on a Full Frame body) of 150mm - 200mm.
Shutter speed would be 1/200th+
ISO 800 (I NEVER use Auto ISO)
Aperture may not be that large, as the lens is long-ish, could be 3.5f ish
The vignette looks fake