We report on the first ESR study of atomic hydrogen and tritium stabilized in solid T₂ and T₂:H₂ matrices down to 70 mK. The concentrations of T atoms in pure T₂ approached 2 × 10²⁰ cm^-3 (0.60%) and record-high concentrations of H atoms ∼1 × 10²⁰ cm^-3 (0.33%) were reached in T₂:H₂ solid mixtures where a fraction of T atoms became converted into H due to the isotopic exchange reaction T + H₂ → TH + H. The maximum concentrations of unpaired T and H atoms were limited by their recombination which becomes enhanced by efficient atomic diffusion due to the presence of a large number of vacancies and phonons generated in the matrices by β-particles. Recombination also appeared in an explosive manner, both being stimulated and spontaneously in thick films where sample cooling was insufficient. We suggest that the main mechanism for H and T migration is physical diffusion related to tunneling or hopping to vacant sites in contrast to tunneling chemical exchange reactions which govern diffusion of H and D atoms created in H₂ and D₂ matrices by other methods.