cdf ratio and mean estimation

Dear all,

I need to know if is it possible to find the mean of a normal distribution knowing the ratio of the area under the "bell" curve on the left and on the right of a given point.

To be more precise I need to solve the following equation

$\displaystyle \frac{1}{\sigma \sqrt{2\pi }}\int_{x=\bar{X}}^{+\infty }\exp \left( \frac{\left( x-\mu \right) ^{2}}{2\sigma ^{2}}\right) dx=\frac{k}{\sigma \sqrt{2\pi }}\int_{x=-\infty}^{\bar{X} }\exp \left( \frac{\left( x-\mu \right) ^{2}}{2\sigma ^{2}}\right) dx$

where I know the ratio $\displaystyle k$, the variance $\displaystyle \sigma ^{2}$ and the point $\displaystyle \bar{X}$ is fixed. i need to find the mean of the distribution $\displaystyle \mu$ that achieve the ratio of $\displaystyle k$ between the two portion of area.

thanks in advance.