My answer uses only CSS, and it does not use overflow:hidden or display:table-row. It requires that the first child really does have a given height, but in your question you state that only the second child need have its height not specified, so I believe you should find this acceptable.
html
<div id="container">
<div id="up">Text<br />Text<br />Text<br /></div>
<div id="down">Text<br />Text<br />Text<br /></div>
</div>
css
#container { width: 300px; height: 300px; border:1px solid red;}
#up { background: green; height: 63px; float:left; width: 100% }
#down { background:pink; padding-top: 63px; height: 100%; box-sizing: border-box; }