I'm using Blender 2.8 (Windows 10). I have two collections. One With a plane that I would like to hold a projection of an image I would like to convert into an object. The other collection with the object I am modelling. Somehow the wedge object is unselectable and I can only select the plane object. Trying to access it from the objects list and choosing "select" just results in the image below (but does not allow me to edit it using the "Edit mode" options.
This is a classic gotcha.
If you see this in the 3D viewport ...
You're still in Edit Mode and although it looks like you've selected another object, you really haven't ... you've added a secondary object to the selection.
Hit the TAB key to go back to Object Mode, then you should be able to select objects normally again.
Alternatively if you want to stay in edit mode but switch objects then you can simply click the Edit Mesh toggle in the outliner.
This is a real pain in the -Z, something I hope is addressed in the future. It catches me out daily.
Notice in the right hand side the word "Plane" is in orange but the "Wedge" is in grey. If you click the down arrow to the left of "Wedge" and then click the green icon or the text then you can edit the wedge object. I don't know what the orange triangle icon vs green triangle item means yet. I also don't know if this is a bug / feature though it's pretty confusing.
Alternatively if you change the editor type to "Object Mode", then click the "Wedge" text or click the wedge object in your scene. Then change to "Editor Mode" it will then let you edit the wedge object you see (same as Merlin's answer but without the nice keyboard shortcut)
OR, if you right click "Wedge" text and choose "Select", then change to "Object Mode" and back to "Edit Mode" you can now edit both objects.