Installation failed with error: 0x80070656. The operating system reported error 2147944022: Error opening installation log file
This software was deployed regularly using Install Software SCCM Task Sequence component.
After spending some time with testing and log analyzing, I tried Command line Task Sequence component where I specified setup.exe command, the package and credentials for admin user.
After TS launching, the issue was successfully resolved and HP WebCam software installed on the machine.