How can I distinguish E1 from E2?

How to distinguish a E1 reaction from an E2 reaction? 

E1 reaction and E2 reaction differ in the order of their rate equations with respect to the base, one one to discover which reaction we are looking at is to plot a graph of the variation of rate with base concentration. This can be very difficult with E1 because it needs just a very week base, usually the same solvent is the base. 

More detailed differences between reaction mechanisms comes from studying the rates of elimination in substrates that differ only in the substitution of one or more proton with deuterium. These differes are known as kinetic isotope effects.  

Usually it is said that isotopes of an element are atoms that differ only in the number of neutrons in their nuclei and that they are chemically identical but for hydrogen it is not true. Infact the chemical difference is significant, if you think about it no other element has an isotope which is twice as massive as the other. 

So far kinetic isotope effects are the changes in rate observed when an (1H) hydrogen atom is replaced by a (2H) deuterium atom in the same reaction.  

For any reaction the kinetic isotope effect is defined as:

KIE= k(1H)/k(2H) 

To change H for D has an effect on the reaction rate only if that H or D is involved in the rate-determining step.