Potential difference,V, is the electric potential energy per charge.  That is, what does is cost to place a charge in that location?  If it costs 30J to put 3C at a spot, then its potential difference is 10 J/C or 10 volts.

V = PE / q_test

    It takes work (energy) to place two protons together.  Therefore, when you move a positive charge nearer another positive charge you have given it more energy.  Because potential difference is the energy per charge, the potential difference of the positive test charge has also increased.  On the other hand, when you bring a negative charge nearer a positive, it has less ability to make a change, so its energy--and its potential difference-- has decreased. 

     To increase potential energy of an object, you must do work on that object.  That is, you put a force on it and push it a distance to give it that PE.  This means:

V = Fd / q_test     but d= the distance moved (same as r)  and F = Coulomb's force = kq₁q₂/r²  so this equation becomes...

V = kq/r

Or, using the fact that E = kq/r²,

V = Ed