I figured it out. What was mentioned above is correct. The tr means that the value is a transform and the ! means that the transform is inverted. The transform that is used here is a homogeneous transformation matrix. I attached an example.
After I figured out how the transform worked, I needed to know what values the matrix consisted of. I attached a sketch where I explain which transforms fills the matrix. The most important thing in this sketch is that the matrix for trSphere and trCenter use the same orientation. This means that the rotation part of both matrices is the same before trSphere is inverted. The last collum of the matrices need to be filled with the location of a point on the sphere for trSphere and the location of the reference point for trCenter.
Finally, trSphere is inverted and is multiplied with trCenter. This gives back a matrix trTempTool. The last column of the matrix gives the temporary TCP. In the Staubli code this is done four times. The 4 calculated values for the TCP are then added up and divided by 4. This gives the average of the 4 temporary TCP's. This average is the final TCP.
I attached a Matlab file with the calculator I made for determining the TCP.
//Inverse sphere * center
for l_nI=0 to 3
Thank you for helping me solve this problem.