Play Eadd9 one string at a time and you hear E, G#, B and F#. E is the root, G# the major third, B the fifth and F# the ninth. Said aloud, its notes are E, G sharp, B and F sharp.
From the low string to the high one you hear E, B, E, G#, B and F#. Of the six strings you play, two give E, the note that names the chord. The lowest note is E on string 6 and the highest is F# on string 1.
Eadd9 lets two strings ring open. String 6 gives E and string 2 gives B. Everything fits between frets 1 and 2. The second shape on this page starts at fret 1.
E is one change away. String 1 is left open, bringing in E, the root of E. It shares two notes with C#m, E and G#. The change that keeps the most fingers still is to B7. Two stay in place.
Eadd9 shows up in six keys. In E major it is the Iadd9, in A major the Vadd9 and in B major the IVadd9. The rest appear in the key list.