  In this letter, we present the performance of a $100~\mu\mathrm{m}\times
400~\mu\mathrm{m} \times 40~\mathrm{nm}$ tungsten (W) Transition-Edge Sensor
(TES) with a critical temperature of 40 mK. This device has a measured noise
equivalent power (NEP) of $1.5\times 10^{-18}\ \mathrm{W}/\sqrt{\mathrm{Hz}}$,
in a bandwidth of $2.6$ kHz, indicating a resolution for Dirac delta energy
depositions of $40\pm 5~\mathrm{meV}$ (rms). The performance demonstrated by
this device is a critical step towards developing a
$\mathcal{O}(100)~\mathrm{meV}$ threshold athermal phonon detectors for
low-mass dark matter searches.
