Resolution is basically the same word as determination. When we make a determination we make a promise to ourselves, "I want to do something," that is our resolution.
For example, in the Ten Paramis talk, I mentioned making a New Year's resolution concerning the Paramis. When we make a resolution, it is a shift in our mind, we want to do something, usually something new, something better hopefully, to improve our life or to help. So, it is a shift in our mind and it is a thought of, "I want to do this."
Now we can make all sorts of resolutions and they never get done, unless we have energy behind the resolution. This is the important connection between resolution and energy. That is, once we become resolute to do something, we become determined for some new direction, which is hopefully beneficial in our life, then we have to put forth the energy to get it done.
Does the increase in one necessarily mean an increase in the other, regarding energy and resolution? It is hard to say that as a black and white answer. For some people it will work that way, that we resolve something, we put our energy behind it, we succeed and then we are so happy that we succeeded in one thing. Then we make another resolution, we put our energy behind it, and then we succeed again. So, if things do work in that way, that is great. That way we are continually putting forth a new direction, a new thought to improve our life, we continually get that energy in there, we succeed, we want to do more and more and more.