An object in motion tends to stay in motion (Newton’s First Law of Motion). There is no significant friction or drag in space to slow it down and so adding energy is not required. In fact, energy would need to be used for it to slow down.
The Earth’s motion is leftover from from the motion of the cloud of matter that formed the solar system. That cloud condensed into the sun and planets due to gravity. The relatively high speed of Earth’s rotation (both around itself and around the sun) is a result of that process.
This is described by the conservation of angular momentum, where matter rotating slowly when spread out will rotate more quickly when it is condensed. A common demonstration of this is a spinning figure skater whose rotation speed increases or decreases as they move their arms inward or outward.
The mistake in this thinking is that you are used to movement on Earth, not in space. Here on Earth, a car needs to spend fuel to keep moving, because the air drag and tire friction and engine resistance etc. are slowing it down.
In space, nothing is slowing you down. If you already move at some speed and you don’t spend any energy on altering that movement, you will just keep on moving at that speed forever.
So the question you should be asking is not how the Earth keeps rotating and moving, but rather what made the Earth rotate and move in the beginning. And the answer to that is how the solar system formed: Out of a huge spinning cloud of gas, which condensed into small spinning lumps of gas and rock. Earth is one of those lumps, and thus keeps on spinning (around itself and around the Sun) forever.
*) obviously not really forever, and all of this is a simplification, but it should do for an ELI5.
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