The drilling core sampling and chemical analysis method for the quantitative determination of solid mineral deposits has several drawbacks, including a low core drilling efficiency, a high core sampling cost, and a long chemical analysis cycle. In current uranium quantification practices, advanced techniques have been developed to preliminarily determine the formation of uranium content based on the interpretation results of natural $\gamma$-ray total logging. However, such methods still require supplementary core chemical analysis to derive the uranium–radium–radon balance coefficient, which is then used for equilibrium correction to obtain the true uranium content within the uranium-bearing layer. Furthermore, conventional prompt neutron time spectrum logging is constrained by low count rates, resulting in slow logging speeds that fail to meet the demands of practical engineering applications. To address this, this study proposes a uranium quantification method that corrects the natural $\gamma$-ray total logging using prompt neutron time spectrum logging. Additionally, a calibration parameter determination method necessary for quantitative interpretation is constructed. Experimental results from standardized model wells indicate that, in sandstone-type uranium deposits, the absolute error of uranium content is within $\pm 0.002\%\mathrm{eU}$, and the relative error is within $\pm 2.5\%$. These findings validate the feasibility of deriving the uranium–radium–radon balance coefficient without relying on core chemical analysis. Compared with the prompt neutron time spectrum logging method, the proposed approach significantly improves the logging speed while producing results that are essentially consistent with those of natural $\gamma$-ray total logging. It provides an efficient and accurate solution for uranium quantitative interpretation.