得る

「得(え/う)る」expresses the possibility of something happening, or the ability to do something in a specific situation.
On the other hand, 「得(え)ない」expresses the impossibility of something happening, or the inability to do something in a specific situation.
The kanji 得 in 「得る」has two readings, え or う, but in other forms (such as 「得ます」「得ない」...), it only has the reading え.
This structure is often used in writing, but the phrases「あり得る」and「あり得ない」are commonly used in daily conversations.
Note: This structure is not used to express purely skills or abilities (like playing an instrument, riding a bike, cooking...).