  We map the three-body problem in two dimensions onto one particle in a three
dimensional potential treatable by a purposely-developed
boundary-matching-matrix method. We evaluate binding energies of trions
$X^{\pm}$, excitons bound by a donor/acceptor charge $X^{D/A}$, and overcharged
acceptors/donors in two-dimensional atomic crystals of transition metal
dichalcogenides, where interaction between charges features logarithmic
behavior at intermediate distances. We find that dissociation energy of
$X^{\pm}$ is, typically, much larger than that of localised exciton complexes,
so that trions are more resilient to heating, despite that their recombination
line in optics is much less red-shifted from the exciton line, as compared to
$X^{D/A}$
