Mechanically, from a corporate finance perspective, the price per share doesn't change. Equity decreases or increases by the amount of the buyback or issuance. So in your example, a buyback of 1 share means equity becomes $90, and each share is still worth $10. Likewise for dilution, equity goes up to $110, share still remains at $10. The dilution refers to the ownership of the company, not the stock price.
However, in markets, a buyback is a positive signal (with increased EPS also) that can increase the share price.
However, in markets, a buyback is a positive signal (with increased EPS also) that can increase the share price.