The reason that appendChild is not a function is because you’re executing it on the textContent of your p element.
You instead just need to select the paragraph itself, and then append your new text node to that:
var paragraph = document.getElementById("p");
var text = document.createTextNode("This just got added");
paragraph.appendChild(text);
<p id="p">This is some text</p>
However instead, if you like, you can just modify the text itself (rather than adding a new node):
var paragraph = document.getElementById("p");
paragraph.textContent += "This just got added";
<p id="p">This is some text</p>