Kepler's equation is a bit like this [1]. A body is moving in a known elliptical orbit, and you would like to know where it is at any given time - eg a quarter of the way through its orbit (so going from 'mean anomaly' to 'eccentric anomaly'). The starting point is a handful of simple equations, of motion and gravitation. But there is no analytical expression that answers the question - you have to solve it numerically, or approximate it with a sufficiently accurate Taylor series.

https://en.wikipedia.org/wiki/Kepler's_equation