I had this issue on my iPad and, as the Outlook account was a waste of space unless I could enter my password, I deleted it (Settings/Mail/Outlook/Delete Account).
I then tried adding the account (Settings/Mail/Add Account/Outlook.com) but I couldn't get it to work.
So I gave in and set it up manually:
Settings
Mail
Add Account
Other (NOT Outlook.com!)
Add Mail Account
Name (the name you want to be known by)
Email (your email address)
Password (your Outlook password - the one you've been trying and failing to enter)
Description (Outlook)
Then it requests some incoming server info:
Host Name (outlook.office365.com)
Username (your email address)
Password (should be filled in from previous screen)
and some outgoing server info:
Host name (smtp.office365.com)
Leave the rest blank and continue.
Worked for me. :-) Good luck!