I had a little experience with this code when I rebuilt my tranny. The code is saying that the TFP switches are not giving the correct combination of highs and lows (voltage there or not there) for the individual gears that the shift selector is in. For example, if you are in the "D" position, a unique combination of the TFP switches are made. If these switches don't match up to the internal program in the PCM, then it flags the P1810 code. All of the wires from the TFP are passing throught the 20-pin connector located on the top of the tranny. If you have a scanner to look at this data, it's a simple matter of looking at the truth table (the combination of the high's and low's) as you go through each gear. This info is located in the service manual for the car or in the ATSG manual.
If you don't have a scanner, you'll have to use a voltmeter and backstab through the 20-pin connector to get access to these combinations through each gear. You'll have to be sure of course that you do have the +12V and ground for the switch. I'm at work now, so I don't have the diagram and truth table in front of me.
In my case, I rebuilt the tranny and even bought a new TFP switch. I even checked it out on the bench before I installed it. Everything looked good! After I cranked the engine, the check engine light came on. I got the P1810 code even with my careful preparation in checking it. Through a TechII scanner I own, I had an invalid combination of switches in Drive. After checking the wiring and finding nothing was wrong there, I knew something was wrong with the switch. So, I dropped the tranny down to remove the side cover and took the switch out. From the wiring diagrams, I knew the switch position and saw that the O-ring around the membrane switch was compressed. Of course, when you torque the TFP down, the o-rings will compress, but in this case, it actually made a NO switch a NC switch which would never release.
In the end, I bought a new switch, torqued it down and before I bolted the side cover on, I checked all the switches to be sure the combination was correct. That took care of the problem.
Sorry for the long post, but I feel that the more information one has, the better suited he/she can tackle a problem and get it solved.
Terry