You need an extra div to warp your div#distance tag.
HTML:
<body>
    <div id="leftSide">
        <p>orange</p>
    </div>
    <div id="rightSide">
        <div class="div-p">
            <div id="distance">apple</div>
        </div>
        <div id="googleMap"></div>
    </div>
</body>
CSS:
html, body {
    margin:0;
    padding:0;
    height:100%
}
.div-p {
    height: 20%;
    text-align: center;
    font-size: 2em;
    display: table;
    width: 100%;
}
body {
    width:100%;
    margin:0;
    display:table;
    border-collapse:collapse;
    table-layout:fixed;
}
#leftSide {
    display:table-cell;
    vertical-align:middle;
    width:2em;
    font-size:4em;
    padding:0;
    overflow:hidden;
    background-image: url('eiffeltower.jpg');
}
#leftSide p {
    display:table;
    text-indent:1.75em;
    white-space:nowrap;
    transform:rotate(-90deg) translate(-50%, 0);
    transform-origin:1em center;
}
#rightSide {
    height: 100%;
    margin:0;
    padding:0;
}
#distance {
    display: table-cell;
    vertical-align: middle;
}
#googleMap {
    height:80%;
    background-color: yellow;
}