<div id="container">
    <div id="first_child" style="width:350px; height:350px;">&nbsp;</div>
    <div id="second_child" style="width:???px; height:350px;">&nbsp;</div>
</div>

#container {
    width:89%;
    height:350px;
}
#first_child {
    float:left;
    width:350px;
    height:350px;
}
#second_child {
    height:350px;
    margin-left:350px;
}

#second_child {
   width: -moz-calc(100% - 350px);
   width: -webkit-calc(100% - 350px);
   width: calc(100% - 350px);
}

var containerWidth = $('#container').width();
$('#second_child').width(containerWidth - 350);

// This is assuming there is no padding.
totalWidth = document.getElementById('container').offsetWidth;
firstChildWidth = document.getElementById('first_child').offsetWidth;
document.getElementById('second_child').style.width = (totalWidth - firstChildWidth) + 'px';

#container {
position:relative
}

#first_child {
width:350px;
height:350px
}

#second_child {
height:350px;
position:absolute;
top: 0;
left:350px;
right:0;
}