Turbulent jets are canonical flows which have been extensively studied in the past. However, reliable analytical expressions for Reynolds stresses and turbulent kinetic energy budget terms are still lacking. In this work, a theoretical analysis of the plane turbulent jet in the self-similar regime is carried out to fill this gap. We first propose a more complete form of the momentum equations (termed as “augmented similarity equations”), whereby the mean momentum and Reynolds stress terms are retained while the viscous and pressure terms are dropped. We then show that it is possible to solve the resulting streamwise and cross-stream momentum equations under the single assumption that the mean streamwise velocity profile is Gaussian in nature. This novel approach allows obtaining expressions for both Reynolds normal and shear stresses, and subsequently for obtaining the turbulent kinetic energy budget terms. The calculation of the Reynolds stresses based on the proposed expressions compare well with their experimental and direct numerical simulation (DNS) counterparts. Further, the analytical expressions of the individual terms of turbulent kinetic energy budget are shown to compare well with the available experimental and DNS data. In our approach, all budget terms are actually calculated and not obtained indirectly by applying an energy balance, as is often done. The proposed analytical expressions, and in particular those of the turbulent kinetic energy budget terms, should help future theoretical analysis of turbulent jets.