Gd- and Fe-based contrast agents reduce T and T relaxation times, respectively, are frequently used in MRI, providing improved cancer detection. Recently, contrast agents changing both T/T times, based on core/shell nanoparticles, have been introduced. Although advantages of the T/T agents were shown, MR image contrast of cancerous versus normal adjacent tissue induced by these agents has not yet been analyzed in detail as authors considered changes in cancer MR signal or signal-to-noise ratio after contrast injection rather than changes in signal differences between cancer and normal adjacent tissue. Furthermore, the potential advantages of T/T contrast agents using image manipulation such as subtraction or addition have not been yet discussed in detail. Therefore, we performed theoretical calculations of MR signal in a tumor model using T-weighted, T-weighted, and combined images for T-, T-, and T/T-targeted contrast agents. The results from the tumor model are followed by in vivo experiments using core/shell NaDyF/NaGdF nanoparticles as T/T non-targeted contrast agent in the animal model of triple negative breast cancer. The results show that subtraction of T-weighted from T-weighted MR images provides additional increase in the tumor contrast: over two-fold in the tumor model and 12% in the in vivo experiment.