In this brief exposition we develop novel general formulae for distributions that are central to excursions of a diffusion process. We consider any scalar time-homogeneous solvable diffusion straddling two arbitrary levels within a finite time T and allow for general endpoint boundary types. In particular, we derive general formulae for both the marginal distribution of the first hitting time (post-T) to a given level and its joint distribution with the last hitting time to another level within time T. Our formulae involve only univariate integral expressions that are readily implementable for any solvable diffusion. We demonstrate their applicability by easily reproducing known formulae for standard Brownian motion. We also present general formulae for any solvable model arising from a Doob-transform.