I have been working with Origin pro 8.5 to do XPS analysis. However, I am not really sure how to calculate atomic composition of each element using origin.
In Origin, you need to perform the following steps:
1) For a chemical shift analysis, perform the peak fitting as described by Muhammad Aslam Baig
after subtracting a background (Shirley is standard and available in Origin).
2) If you want to perform a full stoichiometric analysis, you need to normalize the element signals as described in
http://uhv.cheme.cmu.edu/manuals/M470101.pdf
beginning on page 67. If you use uncoupled peaks, exclusively, e.g. just O1s instead of the O2p1/2 and 3/2, I would recommend the Yeh cross sections instead of the Scofield ones. For all other constants, you can follow the recommendations in the linked manual.
Edit: by the way: using special XPS software actually isn't the worst idea, so if you have that option, use it.