overflow: hidden behind padding

/*** USELESS STYLES ***/
html,
body {
  background: #FFF;
  margin: 0;
  padding: 0;
  font-family: sans-serif;
  font-size: 14px;
  line-height: 1.4em;
}
.element:before {
  content: '> ';
}
/*** .USELESS STYLES ***/

.element {
  background: #F1F1F1;
  color: #555;
  padding: 10px 15px;
  overflow: hidden;
  border: 1px solid #ccc;
  margin: 10px;
  text-overflow: ellipsis;
  white-space: nowrap;
  width: 50%;
}

<div class="element" title="This is some text that will need to cut because it will be far to long for users to see but the user should know what it means, and they can even click to find out more about this if your site supports this.">Hover Over Me. This is some text that will need to cut because it will be far to long for users to see but the user should know what it means, and they can even click to find out more about this if your site supports this.</div>

table {
   width: 100px;
    table-layout:fixed;  
}

td {
  border: 1px solid red;
  padding: 10px;
}

.inner {
    border: 1px solid blue;
    overflow: hidden;
    text-overflow: ellipsis;
}

<table>
    <tr>
        <td><div class="inner">123456789012345678901234567890</div></td>
    </tr>
</table>