I think the question is self-explanatory but stackexchange requires me to write something here.
(As to why he chose the letter $T$, no idea. Words like kinetic, energy, work, appeared only later.)
Gaspard-Gustave Coriolis and Jean-Victor Poncelet used the name "quantité de travail" (quantity of work) and "travail mécanique" (mechanical work) to denote the kinetic energy. I guess that this (the term "travail") could be the origin of the symbol $T$. See at the end of https://en.wikipedia.org/wiki/Vis_viva
(Be patient for my superficiality, I am very far from being a historian of science, I am just a mathematical physicist and this post migrated here from PSE.)