There are a number of questions there.
"Can LED light provide same amount of energy as sunlight?"
In total, no, at least with humanity's available resources. The sun is kinda big. Per unit area? Sure, if you use enough LEDs and focus them tightly enough.
"Can humanity get rid of the sun"
Probably not, within our currently available technology ;-) Even destroying the Earth is a hard problem.
"...and charge solar panels from LED light alone? If this is feasible, this would be
truly sustainable energy. Have two panels of the same size, bottom one made of solar
panel and the top panel made up LED light. Two panels facing each other."
No. What you are suggesting is a perpetual motion machine (only without the motion). The efficiency of photovoltaic panels is somewhere in the region of 15%, so about 85% of the light energy is lost rather than being converted to electricity. The efficiency of the LEDs is also far short of 100%, so not all of the electricity is converted back to light.
Morover, the second law of thermodynamics means that no matter how good technology gets, neither of these devices will ever be 100% efficient, so this will never work.
(In this context, a simple and helpful way in which to think of the 2nd law is perhaps: "You can't get back more than what you put in. In fact, you can't even get back what you put in")
(apologies to anybody who finds this answer too flippant. I'm in that sort of mood!)