Dense hydrous magnesium silicate (DHMS) phase E is a potential water carrier in subducting slabs that can transport water to the Earth's deep mantle between the bottom of the upper mantle and the uppermost transition zone. Therefore, knowledge on the high pressure-temperature (P-T) full elastic moduli of phase E at relevant mantle conditions is important in deciphering the existence of DHMS phases and their influences on seismic profiles in the region; however, the high P-T elasticity data of phase E still remains lacking. In this work, we determined the combined effect of P-T on the single-crystal elasticity of phase E up to 24 GPa and 900 K by in situ X-ray diffraction and Brillouin scattering measurements in externally-heated diamond anvil cells. The aggregate elastic moduli and compressional-wave (V-P) and shear-wave (V-S) velocities of phase E are then derived by analyzing the single-crystal elasticity and density data using the third-order finite-strain equations. We found that phase E exhibits much lower bulk and shear moduli and acoustic velocities than the most abundant constituent minerals in the upper mantle and transition zone, such as olivine, clinopyroxene, garnet, and wadsleyite. The modeled results using the obtained elasticity results show that the existence of phase E in a hydrated pyrolite model can result in relatively lower Vp and Vs profiles and negative velocity anomalies in seismic observations. The existence of phase E with relatively lower velocity profiles could be a possible origin of the low-velocity layers atop the 410-km discontinuity in some cold and highly-hydrated regions.