Is the $\Delta E$ due to the potential difference in the depletion zone? In an unbiased condition, why is equilibrium not established before a depletion zone can form?

Yes, for an unbiased p-n junction, the $\Delta E$ is due to the potential difference in the depletion zone. When p-type and n-type are stuck next to each other there is a thermally-driven diffusion of electrons from n to p type, and of holes from p type to n-type near the boundary, which establishes a separation of charge (excess negative charge on the p side and excess positive charge on the n side). The diffusion happens until enough charge has built up to create an electric field that prevents further charge buildup - that's when equilibrium is established, and flow is balanced in each direction. At equilibrium, there is non-zero charge separation and a depletion zone in the region near the boundary, from which the charge carriers have drifted. This configuration, with a potential difference and electron energy increase on the p-side, has required energy input to the system. This energy comes from thermal energy in the environment for an unbiased junction-- in this configuration a non-zero diffusion results in a $\Delta E$. (A battery provides energy for a biased junction.)