The energy equation is straight forward, yes, but is there an intuitive reason for this?
Just think about it. The wavelength is the inverse of the frequency, so the shorter the wavelength, the higher the frequency. Photons in the visible electromagnetic spectrum are generated by an oscillation of charge currents. Consequently, because these oscillations are proportional to the frequency of the light wave, more oscillations yield a higher energy. So basically, it takes more energy to make something oscillate "a lot" than to make something oscillate "a little." Thus, with more energy, the photon can transfer that energy more easily.