It can totally be written without "algebra"; it's not the notation that contains the idea, it's only the idea that happens to be often expressed in this notation. I could use any other notation, or even plain English, to express the idea, if I didn't mind the extra verbosity.
For Example:
1. The Berlin Papyrus 6619 (from 2000-1786 BC Egypt) uses prose [1]
2. The Ancient Chinese mathematical text Zhuobi Suanjing uses both prose and a pictorial notation [2]
3. The Baudhāyana Shulbasūtra (from 800-500 BC), a set of mathematical instructions for use in the construction of Vedic fire-altars, uses Sanskrit prose describing geometric constructions using rope [3] [4].
> The Berlin Papyrus 6619 (from 2000-1786 BC Egypt) uses prose
Just because it's prose doesn't mean it isn't algebra. For example "If you square the lengths of the two shorter sides together and add them up it equals the length of the square of the length of the longer side". That's just algebra with words.
The thing that makes algebra algebra is that you use variables, not constants. "the length of the longer side" is just a wordy variable.
https://avatars.mds.yandex.net/get-zen_doc/48747/pub_5c9e493...