Solution 1:

Wrap the image in a span

<nav class="navbar navbar-default">
    <div class="navbar-header">
        <a class="navbar-brand" href="#">
            <span><img src="#"/></span>
            Ultimate Trade Sizer
        </a>
    </div>
</nav>

span defaults to display: inline

Solution 2:

The correct solution would be to use navbar-text on the h3 and not to use any additional div or span elements:

<nav class="navbar navbar-default">
    <div class="navbar-header">
        <div class="navbar-brand">
            <a href="...">
                <img class="img-responsive" src="/brand.png">">
            </a>
            <h3 class="navbar-text">Ultimate Trade Sizer</h3>
        </div>
    </div>
</nav>

See http://getbootstrap.com/components/#navbar-text for the proper documentation of navbar-text.