  Recently, high entropy alloys (HEAs) have emerged as a new platform for
discovering superconducting materials and offer avenues to explore exotic
superconductivity. The highly disordered nature of HEA suggests regular phonon
required for BCS superconductivity may be unlikely to occur. Therefore
understanding the microscopic properties of these superconducting HEA is
important. We report the first detailed characterization of the superconducting
properties of the noncentrosymmetric ($\alpha$-Mn structure) HEA
{(HfNb)}$_{0.10}${(MoReRu)}$_{0.90}$, and {(ZrNb)}$_{0.10}${(MoReRu)}$_{0.90}$
by using magnetization, specific heat, AC transport, and muon-spin
relaxation/rotation ($\mu$SR). Despite the disordered nature, low temperature
specific heat and transverse-field muon spin rotation measurements suggest
nodeless isotropic superconducting gap and Zero-field $\mu$SR measurements
confirm that time reversal symmetry is preserved in the superconducting ground
state.
