Refrigeration superheat calculator - help needed with math

I am planning on building a refrigerant superheat calculator that i can use at work. You can buy these quite readily but I thought it would be an interesting project to try.

Refrigeration engineers use superheat as one way of determining if a system is running properly. The pressure in the system is measured and then using a table the saturated temperature is found for that given pressure. Pressure temperature chart
That temperature is then subtracted from the actual temperature of the system measured with a thermometer. The resulting difference in temperature being the superheat (commonly around 6K)

I am comfortable with reading the data from sensors with my Arduino Uno and writing to an LCD screen what I am struggling with is converting from a pressure to a temperature. This is where I need help.

I found this calculator online that does exactly what I want. When i view the page source I can kind of follow what is happening i think. But don't know where to go from there.

As far as implementing the conversion in my project I could see two ways of doing this 1) manually insert the pressure/temp chart as some sort of array and parse through it, or 2) pass the sensor data straight to the formula (Which I have found below). As far as what would work/is the right way i don't know, I suspect the formula would be better but i don't know how to go about writing it as code, or in a format that I could give it a pressure variable and receive the corresponding temperature.

If anyone could offer any guidance i would be very grateful, I have tried looking around the internet for examples of this project but couldn't find anything very helpful, and thus I come here on bended knees.

Thank you
Ryan

I have found the formula below. Number 4, Vapour pressure, using the saturated pressure constants. Which is a screenshot of part of this document which has further explanations as to what the constants are and all that.

Can you describe the entire system to watch, and what you want to determine finally?

The temperatures on the heat exchanger inlet and outlet may already allow to determine what you need, with less efforts.