Thermal-desorption spectroscopy (TDS) is widely used to characterize hydrogen-isotope retention in plasma-facing tungsten, but a measured spectrum does not uniquely identify the underlying microscopic defect configurations: different kinetic parameters can produce similar curves, while distinct vacancy-hydrogen configurations may have nearly the same binding energy. To account for these ambiguities, we formulate a Bayesian inversion that determines the range of de-trapping-energy spectra consistent with a measured curve and reports all defect configurations allowed by those energies. Applied to a published deuterium-TDS curve of damaged tungsten, the method successfully resolves two de-trapping-energy peaks centered at 1.58 [1.49, 1.70] and 1.97 [1.87, 2.08] eV, where each bracket contains 90% of the inferred probability. Across the four pre-damage conditions, the changing spectra can be described by the same two energy components while the lower-energy component loses relative weight as pre-damage temperature rises; both features also recur in an independent experiment. Tests on curves with known inputs show that peak temperatures are better determined than the de-trapping energies behind them, and that the inferred energies still correspond to many vacancy-hydrogen configurations. The spectral evolution thus points to changing relative contributions from recurring trapping-energy families, without identifying a unique microscopic defect population.