Can't fit a curve for an exponential function, anyone knows why?

What do you mean by "Excel cannot do it"? Does it crash the program or do you mean that it returns an equation that does not give a good fit of the data?

If by "standard exp function" you mean something of the form y=ae^(bx), then I think the reason it is failing to provide a good fit (assuming it is returning some kind of equation) is that a standard exp function is a straight line on a semi-log plot. If you convert your y-axis to a log scale, you will see that your data are not linear on a semi-log plot. Again, assuming it is returning an equation, I am guessing that a standard exponential is not a suitable equation for the data.

1st thing I'd probably suggest is not really Excel related. Obviously we are not looking at ohm's law or anything like it in this case. I would suggest you go back to your electrical schematic and analyze it for clues to the nature of the curve that would give a good fit. For example, perhaps R is one resistor in parallel with other resistors. From ohm's law and the formula for the overall resistance of resistors in parallel, we might hypothesize and equation of the form E=f(1/R). Beyond that, I'm not real familiar with electrical theory, but I would expect that somewhere in a good circuit analysis should be clues to indicate what equation would give a good fit for these data.