Is the E in Arrhenius equation the change of enthalpy?
The "E" is the height of the thermodynamic potential energy barrier. Which potential that is (enthalpy, Gibbs energy, Helmholtz, or internal energy) depends on the conditions under which the reaction takes place - which thermodynamic state variables are held constant.

For example, in a system where the number of moles, the pressure, and the temperature are held constant (called NPT), then the thermodynamic potential energy (and thus the activation energy) is measured using Gibbs free energy.