The accurate determination of the electron temperature (Te) and density (Ne) is critical for understanding argon plasma characteristics, yet inverse solutions to the collisional-radiative (CR) model often suffer from non-uniqueness, complicating data interpretation. The core contribution of this study is the visualization of band-like solution structures within the CR inverse problem and the development of a practical strategy for handling this non-uniqueness. The results reveal band-like residual regions in the Te-Ne space, representing continuous zones where fitting residuals are insensitive to coupled Te-Ne variations, thereby corresponding to multiple solutions. These regions exhibit a change in monotonicity at Te ≈ 1.77 eV under the Maxwellian assumption, reflecting a transition in the dominant electron-collision kinetics governing the excited states. The structures of these regions are highly sensitive to spectral line selection and EEPF assumptions: higher excited-level sets shift the solutions toward higher Ne to balance the relative population distribution, whereas EEPF assumptions with greater high-energy depletion shift them toward higher Te to maintain the necessary excitation rates. The proposed optimization approach efficiently identifies these solutions while maintaining physical consistency. This strategy resolves the non-uniqueness of the inverse problem, ensuring reliable tomographic determinations of Te and Ne in argon inductively coupled plasmas.