Answer
$\tau = 10.0~s$
Work Step by Step
We can use the following equation to find the time constant $\tau$:
$x(t) = A~e^{\frac{-t}{\tau}}$
$0.368~A = A~e^{\frac{-10~s}{\tau}}$
$0.368 = e^{\frac{-10~s}{\tau}}$
$ln(0.368) = ln(e^{\frac{-10~s}{\tau}})$
$ln(0.368) = \frac{-10~s}{\tau}$
$\tau = \frac{-10~s}{ln(0.368)}$
$\tau = 10.0~s$