Wow! Talk about obscure!
I managed to fix my problem by downloading (FTP) my twentyten/functions.php
I then edited it with a text editor (GEDIT) and saw nothing wrong - however I suspected bad chars at the beginning of the file and/or near the end of the first line where there was a ?> <?php
I carefully placed my cursor at the end of the first line of the file and moved it left until it was to the left of the <?php
I then backspaced up to and including the > of the ?> and then re-added the > and pressed the enter - all that to be sure no non-printing chars were between the ?> and the <?php
I then went to the first line of the file, placed the cursor well into the line and backed up to the < of the <?php - I pressed enter, then used ctl-shift-home to select everyting in the file from there to the top. (Should have been nothing, but apparently it wasn't) - i deleted the selected "spaces".
saving the file and uploading (FTP) back over the previous twentyten/functions.php then going to the login page on my browser.
All is well.
Much of this foolishness could be avoided by using a text editor which would show ALL characters, printing or otherwise.
tl;dr There were non-printing chars in the first line of my twentyten/functions.php
I did NOT put them there - never edited the file before - I have no idea how they got there. Not happy about that.