How to indent after each <br/> but not on the first line?

I have <div> elements that may contain one or several <br/>, i.e., hard line breaks. I would like the text of the new line after each <br/> to be indented, but the first line of the <div> should not be indented.

I first tried div { text-indent: 2rem each-line; }. This indents the text after each <br/>, but it also indents the first line of the <div>. So I tried to remove the indentation of the first line with div:first-line { text-indent: 0rem; }, but this does not work, apparently because text-indent is not an allowed property on the :first-line pseudo-element. Neither can I use a negative margin or padding on the :first-line pseudo-element, it seems. Is there a way to achieve what I want to achieve?

<div>Lorem ipsum dolor sit amet, consectetur adipiscing elit. Nullam placerat metus turpis, et auctor eros porttitor sed.
  <br/>Sed ornare eget metus in interdum. Nulla ut orci eget eros ullamcorper semper.
  <br/>Aliquam fringilla urna lectus, ac vestibulum diam sodales eget.
</div>

So, in this example, "Sed ornare" and "Aliquam fringilla" should be indented, but not "Lorem ipsum". Here is the CSS I tried:

div { text-indent: 2rem each-line; }
div:first-line { text-indent: 0rem; }

Here is a picture of what I am trying to achieve:

A hacky idea using negative margin but only available on Firefox due to the support of each-line

.indent {
  text-indent: 2rem each-line;
}
.indent:before {
  content:"";
  margin-right: -2rem;
}

/* fallback to avoid the overflow */
@supports not (text-indent: 2rem each-line) {
  .indent {
    text-indent: 2rem;
  }
}

<div class="indent">Lorem ipsum dolor sit amet, consectetur adipiscing elit. Nullam placerat metus turpis, et auctor eros porttitor sed.
  <br>Sed ornare eget metus in interdum. Nulla ut orci eget eros ullamcorper semper.
  <br>Aliquam fringilla urna lectus, ac vestibulum diam sodales eget.
</div>