CSS fill remaining width

This can be achieved by wrapping the image and search bar in their own container and floating the image to the left with a specific width.

This takes the image out of the "flow" which means that any items rendered in normal flow will not adjust their positioning to take account of this.

To make the "in flow" searchBar appear correctly positioned to the right of the image you give it a left padding equal to the width of the image plus a gutter.

The effect is to make the image a fixed width while the rest of the container block is fluidly filled up by the search bar.

<div class="container">
  <img src="img/logo.png"/>
  <div id="searchBar">
    <input type="text" />
  </div>
</div>

and the css

.container {
  width: 100%;
}

.container img {
  width: 50px;
  float: left;
}

.searchBar {
  padding-left: 60px;
}

You can realize this layout using CSS table-cells.

Modify your HTML slightly as follows:

<div id="header">
    <div class="container">
        <div class="logoBar">
            <img src="http://placehold.it/50x40" />
        </div>
        <div id="searchBar">
            <input type="text" />
        </div>
        <div class="button orange" id="myAccount">My Account</div>
        <div class="button red" id="basket">Basket (2)</div>
    </div>
</div>

Just remove the wrapper element around the two .button elements.

Apply the following CSS:

#header {
    background-color: #323C3E;
    width:100%;
}
.container {
    display: table;
    width: 100%;
}
.logoBar, #searchBar, .button {
    display: table-cell;
    vertical-align: middle;
    width: auto;
}
.logoBar img {
    display: block;
}
#searchBar {
    background-color: #FFF2BC;
    width: 90%;
    padding: 0 50px 0 10px;
}

#searchBar input {
    width: 100%;
}

.button {
    white-space: nowrap;
    padding:22px;
}

Apply display: table to .container and give it 100% width.

For .logoBar, #searchBar, .button, apply display: table-cell.

For the #searchBar, set the width to 90%, which force all the other elements to compute a shrink-to-fit width and the search bar will expand to fill in the rest of the space.

Use text-align and vertical-align in the table cells as needed.

See demo at: http://jsfiddle.net/audetwebdesign/zWXQt/

Use calc!

https://jsbin.com/wehixalome/edit?html,css,output

HTML:

<div class="left">
  100 px wide!
  </div><!-- Notice there isn't a space between the divs! *see edit for alternative* --><div class="right">
    Fills width!
  </div>

CSS:

.left {
  display: inline-block;
  width: 100px;

  background: red;
  color: white;
}
.right {
  display: inline-block;
  width: calc(100% - 100px);

  background: blue;
  color: white;
}

Update: As an alternative to not having a space between the divs you can set font-size: 0 on the outer element.

I know its quite late to answer this, but I guess it will help anyone ahead.

Well using CSS3 FlexBox. It can be acheived. Make you header as display:flex and divide its entire width into 3 parts. In the first part I have placed the logo, the searchbar in second part and buttons container in last part. apply justify-content: space-between to the header container and flex-grow:1 to the searchbar. That's it. The sample code is below.

#header {
  background-color: #323C3E;
  justify-content: space-between;
  display: flex;
}

#searchBar, img{
  align-self: center;
}

#searchBar{
  flex-grow:1;
  background-color: orange;
  padding: 10px;
}

#searchBar input {
  width: 100%;
}

.button {
  padding: 22px;
}

.buttonsHolder{
  display:flex;
}

<div id="header" class="d-flex justify-content-between">
    <img src="img/logo.png" />
    <div id="searchBar">
      <input type="text" />
    </div>
    <div class="buttonsHolder">
      <div class="button orange inline" id="myAccount">
        My Account
      </div>
      <div class="button red inline" id="basket">
        Basket (2)
      </div>
    </div>
</div>