How to extract separate text nodes with Jsoup?

Several ways. That really depends on the document itself and whether the given HTML markup is consistent or not. In this particular example you could get the td's child nodes by Element#childNodes() and then test every node individually if it's a TextNode or not.

E.g.

Element td = getItSomehow();

for (Node child : td.childNodes()) {
    if (child instanceof TextNode) {
        System.out.println(((TextNode) child).text());
    }
}

which results in

 TextA 
 TextB 

I think it would be nice if Jsoup offered a Element#textNodes() or something to get the child text nodes like as Element#children() does to get the child elements (which would have returned the <br /> element in your example).