Energy stored in between the plates of parallel plate capacitor of area A, separated by distance d is:

Energy stored in a capacitor of capacitance: E = 1/2CV²
Capacitance of parallel plate capacitor = ε₀A/d
Potential difference across parallel plate capacitor due to presence of electric field, V = E × d
Thus, energy stored in capacitor = 1/2(ε₀A/d)(Ed)² = 1/2ε₀E²Ad