Is it possible to have the erase tool have a soft edge, changes tools when I try to apply soft edge

I accept this as the answer then and thank you for the very complete and descriptive answer. Let me ask as I see adjusting opacity is the way to get it to not just erase harshly all or none.... but, a brush tool, when you select the brush you can get a 'feathered' hardness from the center outward to completely soft... That is what I was hoping to get as an eraser tool, but asking for too much I think. Thaks again for the correct answer JJMack.