How to Inverse Between Points with SPCs

I want to calculate a distance and bearing between the two points posted above. I don't want to use any software on the NGS website because I want to learn how to do it manually. Can anyone provide me with any good documentation on how to do that? My office wants to RTK the two points and compare that data with the record data. The entire project we're doing will be referenced to the center of section line defined by the points.