The thermally activated delayed fluorescence (TADF) mechanism has recently attracted much interest in the field of organic light-emitting diodes (OLEDs). TADF relies on the presence of a very small energy gap between the lowest singlet and triplet excited states. Here, we demonstrate that time-dependent density functional theory (TD-DFT) in the Tamm-Dancoff Approximation can be very successful in the calculations of the lowest singlet and triplet excitation energies and the corresponding singlet-triplet gap when using nonempirically tuned range-separated functionals. Such functionals provide very good estimates in a series of 17 molecules used in TADF-based OLED devices, with mean absolute deviations of 0.15 eV for the vertical singlet excitation energies and 0.09 eV [0.07 eV] for the adiabatic [vertical] singlet-triplet energy gaps as well as low relative errors and high correlation coefficients compared to the corresponding experimental values. They significantly outperform conventional functionals, a feature which is rationalized on the basis of the amount of exact-exchange included and the delocalization error. The present work provides a reliable theoretical tool for the prediction and development of novel TADF-based materials with low singlet-triplet energetic splittings.