Planetary systems around solar analogs inform us about how planets form and evolve in Solar System-like environments. We report the detection and characterization of two planetary systems around the solar analogs TOI-1736 and TOI-2141 using TESS photometry data and spectroscopic data obtained with the SOPHIE instrument on the 1.93 m telescope at the Observatoire de Haute-Provence (OHP). We performed a detailed spectroscopic analysis of these systems to obtain the precise radial velocities (RV) and physical properties of their host stars. TOI-1736 and TOI-2141 each host a transiting sub-Neptune with radii of 2.44 ± 0.18 R_⊕ and 3.05 ± 0.23 R_⊕, orbital periods of 7.073088(7) days and 18.26157(6) days, and masses of 12.8 ± 1.8 M_⊕ and 24 ± 4 M_⊕, respectively. TOI-1736 shows long-term RV variations that are consistent with a two-planet solution plus a linear trend of −0.177 m s⁻¹ day⁻¹. We measured an RV semi-amplitude of 201.1 ± 0.7 m s⁻¹ for the outer companion, TOI-1736 c, implying aprojected mass of m_csin i = 8.09 ± 0.20 M_Jup. From the Gaia DR3 astrometric excess noise, we constrained the mass of TOI-1736 c at 8.7_−0.6^+1.5 M_Jup. This planet is in an orbit of 570.2 ± 0.6 days with an eccentricity of 0.362 ± 0.003 and a semi-major axis of 1.381 ± 0.017 au, where it receives a flux of 0.71 ± 0.08 times the bolometric flux incident on Earth, making it an interesting case of a supergiant planet that has settled into an eccentric orbit in the habitable zone of a solar analog. Our analysis of the mass-radius relation for the transiting sub-Neptunes shows that both TOI-1736 b and TOI-2141 b likely have an Earth-like dense rocky core and a water-rich envelope.