E2 rips off a proton and the leaving group in one single step.
Base and substrate collide together, so rate equals k times both concentrations.
E1 waits. Bromide leaves alone, leaving a flat carbocation, the slow step.
Only then does a weak base grab a neighboring proton, forming the alkene.
E2: one step, strong base, both matter. E1: two steps, carbocation first, substrate only.