Untitled

<html>
    <body>

        <div style="float:left;">
            Arbitrarily long title
            <div style="float:right">more...</div>
        </div>

        <div style="width:0px; overflow:visible; white-space:nowrap;">
            Arbitrarily long title
            <div style="float:right">more...</div>
        </div>

        <!-- This sort of simulates what I want, but the title length is arbitrary and I don't want to have to measure the text -->
        <div style="width:120px;">
            Arbitrarily long title
            <div style="float:right">more...</div>
        </div>

    </body>
</html>

<div class="title-block">
  <div>Arbitrarily long title</div>
  <div class="more">more...</div>
</div>

.title-block { float: left; position: relative; padding-bottom: 1em; }
.more { position: absolute; right: 0; bottom: 0; }

<div style="float:left; position: relative">
  <div>Arbitrarily long title</div>
  <div style="position:absolute; right: 0">more...</div>
</div>

<div style="float: left;">
    <div>
        Arbitrarily extra extra long title here
    </div>
    <div style="float:right;">
        more...
    </div>
</div>

<div>
    <div> Business area </div>
    <div> Inernal Audit </div>
    <div style="text-align: right;"><a href="#"> More... </a></div>
</div>

<div class="one">
        Arbitrarily long title Arbitrarily long title
        <div class="two">more...</div>
    </div>

.one{
  width:auto;
  float:left;
  border:thin red solid;
  margin:5px;
}
.two{
  float:right;
}