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

[Ken Nielsen]

For over 30 years now, I have never been able to get Photoshop to have an erase tool apply a soft edge, it always only allows a hard edge circle. If I try to change the tool to a soft edge it changes tools to the dodge tool. My question is it possible at all to have the erase tool have a soft edge so I can 'brush' away parts of a overlay to see the layer underneath in a gradated fashion?

[JJMack · Accepted solution]

Its a brush type tool adjust the brush hardness

[Ken Nielsen]

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.