This is how I look at problems like this. First of all, I believe the answer coud be E1/SN1, but probably is not. The kinetics will depend upon concentration of halide and ethoxide. If the reaction were to be diluted sufficiently, the amount of carbocation that may form would increase. In this case, since it is tertiary and benzylic, more solvolysis would occur than other examples. However, adding concentration to the question is too complicated. We should interpret that listing ethoxide as a reagent means it should have a kinetic effect upon the reaction, meaning it must be E2.