In addition to what Ertain said, you can create a scene that inherits another scene using the menu option "Scene > New Inherited Scene". This will let you create a new scene with the same script and node structure as a base scene, where you may set properties and add additional nodes.
For example, you would make an Entity scene with all nodes that would be common to players and enemies such as sprites, physics and collision nodes, audio stream players, etc. Then you would create Player and Enemy scenes using the "New Inherited Scene" menu option where those two new scenes would inherit from Entity. Any necessary additions and modifications can now be made to the Player and Enemy scenes.
Note that if your base scene has a script (e.g. "Entity.gd") then the inherited scenes will also use this script. If you want the inherited scene to have its own script, the script needs to inherit from the script of the base scene as described in the page Ertain linked to. With your inherited scene in the scene editor, select the root node then in the Inspector select the drop-down for the script property and select "Extend Script".
This will let you create a script that properly extends the original scene script.