Multi-scale gyrokinetic theory and simulations of a toroidal magnetized plasma have revealed the existence of cross-scale interactions of the trapped electron mode (TEM) and the electron temperature gradient (ETG) turbulence. Reduction of the TEM instability growth rate in the ETG turbulence is clearly identified, and is well represented in the form of effective diffusion. A theoretical model based on the stochastic forcing by the ETG turbulence well describes the turbulent diffusion coefficient observed in multi-scale turbulence simulations.