Possibility: double lens?

As you ask it, the answer is no. While it is possible to attach one lens to the other objective to objective (the non-mount ends) that is for a very specific use and wouldn't work with those two lenses anyway.

You may be able to use the Tamron with an extender, such as 2x, which will make it a 36-600 zoom, with corresponding loss of 2 stops of light in the process.

With a DSLR camera you must remove a lens if it has a lens mounted.

So you must remove the 18-55mm lens first. This leaves the camera body.

THEN you may attach any size lens that is made for your camera, such as the Tamron 16-300mm. I personally do not like the TAMRON at least the one I purchased, which was the 18-200mm. Personally it was too heavy to carry around for long periods of time and second the 11x14 test print made at a high f/stop (f/11) was soft and not as sharp as I like. So what I am saying is that when it comes DSLR cameras I do not like the extra long telephoto end of the lense.

You would be off with the 18-55mm lens and then have a 50-to-200mm lens to complete your basic outfit. Remember the DSLR cameras claim to fame is that it can accept many different size lenses.

Sort of.

The answer is no. You can mount only one lens to the camera body but there are converters and adapters that also contain glass pieces (technically a lens but not photographically speaking) which can be attached to the front or back of the existing lens. The most popular examples are the screw-on semi-fisheye lens adapter and the 2X telephoto converter.

With dSLRs, zoom does not matter. What's more important is focal length. If you understand focal lengths, you can achieve what you want to do with a non-zooming lens.

It's not possible to stack lens as you suggest but there are a kind of lens, called teleconverters, that mount between a conventional lens and the camera to provide additional zoom range.

No, you cannot put to lenses together. You can, however, use a teleconverter to increase the focal length of the attached lens by either 1.4x or 2x.

There are tele-adapters that fit between the lens and the camera.

That's as good as it gets in practical terms.

Sure, it's called a teleconverter.

The combo you're describing is not possible.

no

No, no, no!