  Using 2.93 fb$^{-1}$ of $e^+e^-$ collision data collected with the BESIII
detector at a center-of-mass energy of 3.773~GeV, we measure the absolute
branching fractions of the decays $D^0\to K^-e^+\nu_e$ and $D^+\to \bar K^0
e^+\nu_e$ to be $(3.574\pm0.031_{\rm stat}\pm 0.025_{\rm syst})\%$ and
$(8.70\pm0.14_{\rm stat}\pm 0.16_{\rm syst})\%$, respectively. Starting with
the process $e^+e^-\to D\bar{D}$, a new reconstruction method is employed to
select events that contain candidates for both $D\to \bar Ke^+\nu_e$ and $\bar
D\to Ke^-\bar \nu_e$ decays. The branching fractions reported in this work are
consistent within uncertainties with previous BESIII measurements that selected
events containing $D\to \bar Ke^+\nu_e$ and inclusive hadronic $\bar D$ decays.
Combining our results with the lifetimes of the $D^0$ and $D^+$ mesons and the
previous BESIII measurements leads to a ratio of the two decay partial widths
of $\frac{\bar \Gamma_{D^0\to K^{-}e^+\nu_{e}}}{\bar \Gamma_{D^{+}\to \bar
K^{0}e^+\nu_{e}}}=1.040\pm0.021$. This ratio supports isospin symmetry in the
$D^0\to K^-e^+\nu_e$ and $D^+\to \bar K^0 e^+\nu_e$ decays within $1.9\sigma$.
