It is fundamentally impossible to obtain the accelerating voltage from the magnification. What a strange question? :) Just ask people who took the images. Sometimes parameters can be attached to the image file or save separately as a text file with the same name. Usually a TEM works with one accelerating voltage long time and there are not any reasons to change it often. Just ask the facility people.
In general, magnification is not a good parameter for pictures - e.g. it depends on the size of the monitor which you use. A scale bar is better and easier. Obviously, it is possible to calculate the scale - just divide the physical size of the scale bar (measure on picture with a ruler :)) by its nominal size, e.g. 10 cm scale bar "100 nm" -> magnification is 10^-1 : 10^-7 = 10^6. But it doesn't have any sense.
If you know your sample well enough, for nice and thin crystal film, which the electrons can transmit through, I think you probably can perform an estimated calculation for the working voltage based on your hi-res image, which should has the scale bar burned in the micrograph. For example if you are able to resolve 1 nm feature, what operating voltage is required to resolve that? Definitely you wont be able to resolve that with 80 kV. If you are able to resolve
this assumption would be useful in the case that accelerating voltage is the only variable which affect the resolution. Unfortunately, there are a lot of variables, that may decrease final resolution and in extreme case you can get worse resolution than 1nm even at voltages over 80kV.
I agree with you. Sample itself is the biggest issue when it comes to getting a good high-res image. The other considerations would be how well the alignment of the gun (what type of source) and lenses are. If the issue with TEM is fixed, we would have removed most of the variables and narrow down to the sample itself. Nevertheless, it also depends on the model of the TEM used. The newer TEM models have better lens system with aberration fixed and good camera and setting would lends itself to a better micrograph.