Are enums allowed to have setters in Java?

I have an enum and it has a parameter (field) that is a String. Am I allowed to have a setter for this field?

public enum Blah {
    Monday("a"), Tuesday("b");
}

private final String letter;

Blah(String letter){
    this.letter = letter;
}

Am I allowed to do the following?

public String setLetter(String letter){
    this.letter = letter;
}