Anden = the duck (the definite form of "en and", meaning "a duck") En anden = someone else/another
Anden also means other, but when you want to say another you need to remember to put en in front of anden I guess it's pretty much the same in English as the word "another" is also a combination of the two words an and other
I actually can't think of an example where you would. As it simply means "other", it is never really used on its own. In a way it is much like English as you can say "another eats potatoes" (en anden spiser kartofler) but not "other eats potatoes" (anden spiser kartofler) --> though this would also mean "the duck eats potatoes"
It can be used on its own in its plural form though. Just like you can say "others eat potatoes" in English, you can also say "andre spiser kartofler" in Danish