Here is the solution recommended by Autodesk for this error by manually replacing the DLL files:

  1. Close EAGLE.

  2. Download the ZIP archive suitable for the appropriate OS from Total Commander Win Tools.

  3. Unarchive the downloaded files.

  4. Create back-ups of the files "libeay32.dll" and "ssleay32.dll" from the directory "C:\EAGLE 9.6.2"

  5. Replace "libeay32.dll" and "ssleay32.dll" from the directory "C:\EAGLE 9.6.2" with the corresponding files, unarchived in step 3.

  6. Restart EAGLE and sign back in.

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