What does the term efficient mean?
if you mean in terms of energy then it refers to a device that transfers more useful energy than it wastes if you mean in terms of energy then it refers to a device that transfers more useful energy than it wastes
In my experience when someone used the term "efficient and equitable manner" they are trying to resolve a dispute or solve a personnel problem. What they mean is they want to solve the problem with as little cost in time/money/hassle as possible (efficient) yet at the same time they want to be fair or at least seem fair (equitable) in the way the problem was handled and finally resolved.
Definition of efficient adjective 1(of a system or machine) achieving maximum productivity with minimum wasted effort or expense: more efficient processing of information [in combination] preventing the wasteful use of a particular resource: an energy-efficient heating system 2(of a person) working in a well-organized and competent way: an efficient administrator