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.
Energy
is expendable. Power
is inherent.
If you say you don't have the power to do something, it usually implies you don't have the inherent ability (or authority) to do that.
I don't have the power to lift this.
I don't have the power to suspend you.
If you say you don't have the energy to do something, it implies you can't do it currently, but you may have in the past and/or you can in the future.
I don't have the energy to walk another mile (but I have the power, and can walk after I've rested for a bit)
I don't have the energy to argue with you (I'm able to, but I'm not feeling up to it)
Basically, no energy means you're temporarily not able. No power is more permanent.
In physics, energy is the ability to do work (or the work done), while power is rate of energy output. So if I push a boulder up a hill, I expend the same amount of energy regardless of how long it takes me. However, doing it in a shorter time period requires more power.
I know you're probably not concerned with this technical distinction. But it is good to know. For example, now you know that it is correct to say "The car is very powerful: It can accelerate from zero to sixty in three seconds," and "It required a huge amount of energy to erect the ancient pyramids."