Real-time time-dependent Hartree-Fock (TDHF)/density functional theory (TDDFT) has been gaining in popularity because of its ability to treat phenomena beyond the linear response and because it has the potential to be more computationally powerful than frequency domain TDHF/TDDFT. Within real-time TDHF/TDDFT, we present a method that gives the excited state triplet energies starting from a singlet ground state. Using a spin-dependent field, we break the spin-symmetry of the α and β density matrices, which incorporates a triplet contribution into the superposition state. The α electron density follows the applied field, and the β electron density responds to the perturbation from the changing α electron density. We examine the individual α/β responses during the electron density propagation. Singlet-triplet transitions appear as 'dark' states: they are present in the α/β responses but are absent from the total electron density response.