E2 versus E1:
The E2 elimination takes place with a strong base (like a hydroxide or ethoxide ion) in a protic solvent (like ethanol or water). The E2 reaction is much more common than the E1 elimination and more helpful. All types of alkyl halide can go through the E2 elimination and the method is helpful for preparing alkenes.
The conditions that suit E1 are similar which suit the SN1 reaction (that is a protic solvent and a non basic nucleophile). Hence, the E1 reaction normally only take place with tertiary alkyl halides and will be in competition with the SN1 reaction.