Like other plants, and indeed all animals, trees transmute energy into food (to wit, survival capacity). It can be assumed that trees suffer some energy loss. However, the notion (as belief) that trees emit energy, that is to say, specifically energised wave forms, that can directly serve the human self-healing process has not been scientifically established.
Since an average human consists of approx. 200 trillion physical bits, i.e. molecules, cells, major organs and so on, and each one operates its own energy (possibly vibration) exchange system, hence source, it is not at all clear how the multiple energy sources in such a complex structure as a tree can influence the multiple energy sources in a human.
Notwithstanding the alleged proofs of Kirilian (alleged specific energy forms output) photography, now debunked, researchers have failed to prove beyond reasonable doubt the claims made for energy outflows per se, healing (including animal magnetism, vitalism, Reiki, the uses of Chi energy and so on (and formerly imagined as a ‘universal fluid’ or ‘luminous ether’, now being reborn as the affects of the quantum field)), so that the claims made about the energy of trees should be treated with caution.
However: the wholehearted belief/conviction that ‘tree energy is good for me’ is in fact good for me in that my wholehearted (i.e. @ 100%) belief floods my brain (and body) and by means of selective flooding brings about positive health effects.