Answer
$R = 870~\Omega$
Work Step by Step
We can find the value $R$ of the resistor:
$Q(t) = Q_0~e^{-t/RC}$
$0.10~Q_0 = Q_0~e^{-t/RC}$
$0.10 = e^{-t/RC}$
$ln(0.10) = -\frac{t}{RC}$
$R = -\frac{t}{C~ln(0.10)}$
$R = -\frac{2.0\times 10^{-3}~s}{(1.0\times 10^{-6}~F)\times ln(0.10)}$
$R = 870~\Omega$
