With some of the upgrades in process for the High-Luminosity Large Hadron Collider (HL-LHC) and the use of forward proton detectors in the CMS experiment at the LHC, we can expect to detect and study rare events and perform precision measurements. In this project, we have studied the photon-photon collision at the LHC produced by radiating protons, followed by a muon-antimuon production. We introduced different smearings in our simulated data, corresponding to different levels of precision in the detectors, and then developed an analysis method to keep most of our photon-photon to two muons signal and reject the pile-up background. With this analysis we were able to estimate that we could observe ∼ 1500 signal events over a year of HL-LHC running, while only ∼ 10 background events in the same time period. This was done assuming 30ps time resolution of proton detectors and 40ps in the time resolution of the main vertex of the collision.