Try this: open a terminal and copy these commands:
cd ~/.local/share/Steam/steamapps/common/Eve\ Online/
wget https://launcher.ccpgames.com/eve-online/release/win32/x64/eve-online-1.9.4-full.nupkg
unzip eve-online-1.9.4-full.nupkg -d out
mv out/lib/net45/ app-1.9.4
rm -r app-1.10.0/
in words: you download the last working version directly from CCP, unpack it Steam’s installation folder, then delete the broken version. If none of that makes sense, better wait for CCP to fix it.