Quick answer
God's greatness shows in what He does not explain. A king's shows in what he digs up. The verse gives the same word to both and points them in opposite directions.
Read both lines
Glory appears twice and is the hinge. For God, glory is in concealing, which is a claim most readers find uncomfortable, and the verse does not soften it or promise the concealment is temporary. For a king, glory is in investigation, because a ruler who does not find out what is actually happening cannot govern. So the two halves are not in tension; they are a description of two different offices. God is not obliged to show His work. A king is.
Note that the Hebrew here is אֱלֹהִים, God, not the covenant name, which fits a saying about His sheer otherness rather than His dealings with Israel. The chapter will return to this root at verse 27, where searching out one's own glory turns out to be a different matter entirely.
Related: Proverbs 25:27 · Deuteronomy 29:29 · Proverbs 20:5
New King James Version®, Copyright © 1982, Thomas Nelson. All rights reserved. Full copyright information. Scripture provided by API.Bible.
Go Deeper
If this verse has been used to put weight on you that it was never carrying, ask about it directly.