All Series E lenses¹ are also AI-S lenses. Your Nikon D7000 can use AI-S lenses with manual focusing and automatic exposure. You may be asked to enter the lens' focal length and f-stop into the camera's menu in order to use Matrix metering. Center Weighted Averaging and Spot metering should work without having to enter anything.

If your Vivitar Series One 70-210mm f2.8-4 is also an AI-S type lens it should be safe to mount on your D7000. The lenses you need to be concerned about are the "pre-AI" lenses made before 1977. There are six different versions of the Vivitar Series One 70-210mm. The first two versions were a constant f/3.5 aperture. The third through sixth versions were f/2.8-4. Version three debuted in 1984 and all Nikon versions should be AI or AI-S.

¹ Series E lenses, a budget lens line from the late film era, should not be confused with more recent 'E' type lenses with electronically controlled apertures. They are two very different types of lenses. Series E are manual focus only AI-S lenses that can be used on pretty much any Nikon F mount camera. 'E' type lenses are new lenses with electronically controlled apertures that can only be controlled by Nikon DSLRs made since about 2007. On older cameras, including all F mount film cameras, the aperture can not be stopped down and will always stay wide open when 'E' type lenses are used.