You can wrap your input field into a span, which you position:relative;. Then you add with 
:before content:"€" your currency symbol and make it position:absolute. Working JSFiddle
HTML
<span class="input-symbol-euro">
    <input type="text" />
</span>
CSS
.input-symbol-euro {
    position: relative;
}
.input-symbol-euro input {
    padding-left:18px;
}
.input-symbol-euro:before {
    position: absolute;
    top: 0;
    content:"€";
    left: 5px;
}
Update
If you want to put the euro symbol either on the left or the right side of the text box. Working JSFiddle
HTML
<span class="input-euro left">
    <input type="text" />
</span>
<span class="input-euro right">
    <input type="text" />
</span>
CSS
 .input-euro {
     position: relative;
 }
 .input-euro.left input {
     padding-left:18px;
 }
 .input-euro.right input {
     padding-right:18px;
     text-align:end; 
 }
 .input-euro:before {
     position: absolute;
     top: 0;
     content:"€";
 }
 .input-euro.left:before {
     left: 5px;
 }
 .input-euro.right:before {
     right: 5px;
 }