The J-PARC E36 experiment is aiming at searching for lepton universality violation by accurately measuring the ratio of branching ratio of the K + → e + ν(γ) (K e2(γ)) to K + → μ + ν(γ) (K μ2(γ)) decays. The experiment was performed at J-PARC employing a stopped K + method in conjunction with a 12-sector iron-core superconducting toroidal spectrometer. Charged particle momenta were determined by reconstructing charged particle trajectories in the spectrometer. Particle identification for e + and μ + was carried out using an aerogel Cherenkov counter and a lead-glass Cherenkov counter, as well as by measuring the time-of-flight between TOF counters. The peak structure due to K e2(γ) decay was successfully observed in the e + momentum spectrum after the e + requirement in the PID analysis. The structure dependentradiative K + → e + νγ () events were selected by imposing photon hits in the CsI(Tl) calorimeter or the GSC counter. The experimental spectra were accurately reproduced by the Monte Carlo simulation, indicating a correct understanding of the experimental conditions. The Br() value relative to Br(K e2(γ)) was determined from the and K e2(γ) yields corrected for the detector acceptances. The Br()/Br(K e2(γ)) ratio was derived to be 1.19 ± 0.07 stat ± 0.04 syst in the CsI(Tl) analysis and 1.25 ± 0.14 stat ± 0.04 syst in the GSC analysis.