Here is the solution recommended by Autodesk for this error by manually replacing the DLL files:
Download the ZIP archive suitable for the appropriate OS from Total Commander Win Tools.
Unarchive the downloaded files.
Create back-ups of the files "libeay32.dll" and "ssleay32.dll" from the directory "C:\EAGLE 9.6.2"
Replace "libeay32.dll" and "ssleay32.dll" from the directory "C:\EAGLE 9.6.2" with the corresponding files, unarchived in step 3.
Restart EAGLE and sign back in.