well, you have heard about electrical potential V, V=Ue/q;
thus, Volt= Joules/Coulomb; Joule= Newton*Meter, thus Volt/Meter= Newton/Coulombs, which is the normal unit of the E field. dimensional analysis works.
another approach: let's say we have a space containing an electric field E. at each and every point in this space, a point charge is said to have a particular energy at each point, potential energy U. to move the point charge from one point to another takes some potential energy difference delta-U. so now we have the work done to move it: W= delta-U. let's generalize this for all q by dividing delta-U by q.
delta-U/q= delta-V, we have defined what is known as the voltage potential difference.
so then W/q= deltaV. now, W= F*deltax also since work is force acting over a displacement, but force on an electric particle depends on the field it is in, namely F= qE.
so, F*deltax/q= deltaV
then
q*E*deltax/q=deltaV
thus
E= deltaV/deltax.
we have proved that electricl field E= voltage potential difference deltaV over the displacement, E=deltaV/deltax
