Coherent wave control exploits the interference among multiple waves impinging on a system to suppress or enhance outgoing signals based on their relative phase and amplitude. This process inherently requires the combination of energy exchanges among the waves and spatial interfaces to tailor their scattering. Here we explore the temporal analogue of this phenomenon, based on time interfaces that support instantaneous non-conservative scattering events for photons. Based on this mechanism, we demonstrate ultrabroadband temporal coherent wave control and the photonic analogue of mechanical collisions with phase-tunable elastic features. We apply them to erase, enhance and reshape arbitrary pulses by suitably tailoring the amplitude and phase of counterpropagating signals. Our findings provide a pathway to effectively sculpt broadband light with light without requiring spatial boundaries, within an ultrafast and low-energy platform.