Two Tails, Two Unknowns

A continuous measurement is modelled as $X \sim N(\mu, \sigma^2)$. Two facts about it are known:

$P(X < 40) \approx 0.025 \qquad \text{and} \qquad P(X > 70) \approx 0.16$

Using only the Empirical Rule (about 68% of the distribution lies within $\mu \pm 1\sigma$ and about 95% within $\mu \pm 2\sigma$) together with the symmetry of the normal curve, what are $\mu$ and $\sigma$?