I can't see why you can't compute this (theoretically). Just substitute the values you want to compute at the pdf and cdf. To express x, you just have to rearrange and make x the subject.
Typing up Normal pdf and Normal CDF will take a bit of time. So to get home the message , let me make a fictitious cdf and pdf.
is your CDF
Using your CDF, you work out your pdf. You differentiate CDF to get your pdf.
In this example,
is your pdf
So, the task is just to solve:
So, this is just some basic algebra.
Sometimes, you may not be able to solve the equation explicitly, in which case you can resort to numerical methods.