Finding length of sides of triangles using differences in distance to a common point

I have three co-linear points A, C, & B respectively. The distance between each of the points is known.

I have a point P at an unknown location, perhaps on the same line if possible, but usually always not co-linear with ACB.

The distance from P to C, called 'c', is unknown.

The distance from P to A is a + c, where 'a' is known (and 'c' is still the unknown distance from P to C). I.E., the distance from P to A is 'a' further than 'c' from P to C.

The distance from P to B is b + c, where 'b' is known (and 'c' is unknown). I.E., the same story as with point A.

a and b can be negative, but a+c and b+c are > 0 of course.

What is the distance from P to C ('c')?

Part II

Let's say the distance from P to A is unknown, but the difference to C and the difference to B are known. What is the distance to A?

Thanks,

Dale