Nonradiative energy transfer (NRET) has been extensively studied in colloidal nanocrystal (quantum dots) and nanorod (quantum wires) assemblies. In this work, we present the first account of spectroscopic evidence of NRET in solid thin films of CdSe based colloidal nanoplatelets (NPLs), also known as colloidal quantum wells. The NRET was investigated as a function of the concentration of two NPL populations with different vertical thicknesses via steady state and time resolved spectroscopy. NRET takes place from the NPLs with smaller vertical thickness (i.e., larger band gap) to the ones with a larger vertical thickness (i.e., smaller band gap) with efficiency up to similar to 60%. Here, we reveal that the NRET efficiency is limited in these NPL solid film assemblies due to the self-stacking of NPLs within their own population causing an increased distance between the donor-acceptor pairs, which is significantly different to previously studied colloidal quantum dot based architectures for nonradiative energy transfer.