Time taken by an alternating quantity to reach a particular value for the second time within one cycle
What shape is the signal was my first thought believing you may want some technical or mathematical answer. So now I'm assuming you want to know how would a circuit find the 2nd point within one cycle of an arbitrary waveform.

I am also assuming that the time taken to reach that 2nd point is based on the first point being taken as the datum, t = 0.

The simple answer is use a comparator circuit and a microprocessor that is counting high speed clocks. The first time the point is passed causes the comparator to change state from 1 to 0 OR from 0 to 1. This event can trigger your microprocessor to start counting. The second event will cause the comparator to reverse the zero and one event and this is used to stop the timer.

And now you have a count in your microprocessor that represents the time difference between E1 and E2.

One thing remains to be added. The point in the cycle you were looking for has to be fed into the comparator as an analogue reference point. This can be done from the micro using a DAC. How you inform the micro what value you are looking for is trivial.

Also, of some interest (maybe) is that if the waveform was a single event, it may not have a "2nd point".

Tricky parts: No it's never as easy as it sounds. Since writing the original answer the OP has furnished the question with the frequency and shape; 50Hz and sinusiodal. Does this make it easier? A bit becuase it is fairly low frequency. The main problems remaining are the comparator and the point it switches - if the circuit doesn't include hysterisis then the points will be as exact as the comparator input offset voltage error allows BUT noise can cause "early" or late triggers on E2 and E1 independantly. 

With hysterisis (noise avoidance method) the timing will be out by a factor based on the amount of hysterisis. It's a compromise; and the likely solution (because it is a sinewave) is a good filter to remove noise with a tiny bit of hysterisis.

Comparator response times should be OK but use a fast device - it's easy to lose a few hunderd usecs on a rise time that's a bit sloppy.