C++ define elements of enum somewhere else in the code [closed]

I have a class in C++ with a public member function that I want to accept as argument a limited number of values and, since I want to make it easier for the user of my class to know what to pass to the member, I'm using an enum (but I'm not sure if there is a better solution) to give him a limited and clear set of things to pass to the function. I use this enum because it uses "words" instead of numbers to describe certain things, which is easier for the user of the class.

Two clarifications: 1) the enum, in the .h file, does not assign values to its elements but in reality it should because each of these words corresponds to a number, and 2) at the same time, I want that the user isn't necessarily aware of the numerical values that each "word" in the enum corresponds to. Therefore, I want to assign a value to each enum element somewhere else, for example in the .cpp file.

The enum is public defined in the .h file like this

 enum ITEM{
      item_1,
      item_2,
      item_3
    };

The member function also public (can be called from outside of the cpp file) is defined in the .cpp file as:

void MyClass::memberFunction(ITEM item) {
    switch (item){
       case item_1:
          otherFunction(1); 
          break;
       case item_2:
          otherFunction(2);
          ...
    }
}

Is it possible to define (or have a sort of an override) the value of each item_i in the cpp file? Something like

    ITEM{
      item_1 = 1,
      item_2 = 2,
      item_3 = 45
    };

This would also avoid the switch because in void MyClass::memberFunction(ITEM item) I can simply call otherFunction(item), if obviously all the item_i are of the same type of the argument accepted by otherFunction(item)

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