Can’t do it exactly by remote, but maybe we can get near. It may need a few attempts…
Go to Admin page > Appearance > Widgets, and drag the Search widget into the Header widget area. No widget title.
Next, try the following custom css
.search-form label {display:inline-block}
.search-form .search-field {width:60px; margin-right:10px}
.search-form .search-field:hover {width:206px; -webkit-transition: width 2s}
.search-form input[type="submit"] {margin-top:-10px; padding:0 10px ;border:1px solid #fff}
Feel free to tweak the values to your taste.
For custom css, you can use a plugin like this one:
https://wordpress.org/plugins/simple-custom-css/