How can a short wavelength mean high energy transition?

I guess you are talking about transitions (quantum jumps) between orbitals in atoms. The energy of a photon is directly proportional to its frequency. Einstein worked that out, more than a hundred years ago. Higher frequency means shorter wavelength, of course. read more

So, that means the shorter the wavelength the higher the energy. Light can interact with atoms to raise electrons into orbitals with higher energy levels. So, a short wavelength means that a high energy transition is possible. read more

A high energy light will have a shorter wavelength than a low energy light. If the wavelength goes down, then the frequency goes up. read more

Try a complete sentence. Given two transitions each of which emit (or absorb) a photon, the one which emits the photon of the shortest wavelength looses the most energy. read more