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We report the precise energy scan measurement of the cross section line shape of ψ(2S)→K^{+}K^{-}. The analysis is based on e^{+}e^{-} collision data corresponding to an integrated luminosity of 495 pb^{-1} collected with the BESIII detector at BEPCII. By analyzing the cross section line shape, we extract the relative phase Φ between the strong and electromagnetic amplitudes of the ψ(2S) resonance, a fundamental parameter in charmonium physics, based on the assumption that the relative phase between the electromagnetic amplitude of the ψ(2S) resonance and the continuum is zero. Two distinct solutions for the branching fraction B of ψ(2S)→K^{+}K^{-} are observed: a constructive interference solution with B=(7.49±0.41)×10^{-5} and Φ=(110.1±6.7)°, and a destructive interference solution with B=(10.94±0.48)×10^{-5} and Φ=(-106.8±5.7)°. A significant correlation between Φ and B is established, demonstrating that interference effects must be taken into account in the ψ(2S) branching fraction measurements. Additionally, the first results for both the ψ(2S) strong form factor, which characterizes the strong coupling between ψ(2S) and K^{+}K^{-}, and the energy-dependent electromagnetic form factor of the charged kaon in this energy region are reported.