Output Voltage Formula verification of Operational Amplifier circuit
The above design is an amalgamation of a Wheatstone bridge and a differential amp. It is hard to analyze and IMO an improper way to design a temperature sensor circuit. A better way is to have a wheatstone bridge followed by a diffamp as shown below:


Source: https://electronics360.globalspec.com/article/5424/design-notebook-linearization-of-a-wheatstone-bridge

The equations for that bridge are as follows: 


Source: https://electronics360.globalspec.com/article/5424/design-notebook-linearization-of-a-wheatstone-bridge