How to login when I can't enter my password because "e" key on keyboard doesn't work
Try entering ⌘+option+F5 to bring up the "Accessibility Options" popup window. This window will appear similar to what is shown below.



Select "Enable Accessibility Keyboard", then click on the "Done" button. The on-screen keyboard should appear, as shown below.



Use the keyboard to enter the "E" key or the entire password.