You have an "alloweditranges" assigned to the sheet which I think will supercede the locked/unlocked property. I'm not sure how to remove it without vba but if you press alt+f11 to open the vba editor, click insert-> module and then copy this code:
Sub macro_1()
Sheets("Mileage Log").Protection.AllowEditRanges(1).Delete
End Sub
into it and run the macro (place the cursor on the sheets("... line and press F5).

Then when you protect the sheet column E should be protected