Consider this Mojo::DOM example, I've made some assumptions as your source data does not seem complete:

cat dragnet.pl 
#!/usr/bin/perl
use strict;
use warnings;
use Mojo::DOM;
use feature 'say';

my $html = '<div class="phone">
<div class="icon"></div>
<p class="title">Telephone</p>
<p>0123-4 56 78 90</p>          
<p class="title">Telefax</p>
<p>just the fax ma\'am</p>
</div>';

my $dom = Mojo::DOM->new( $html );
my $phone = $dom->at('div.phone > p:nth-of-type(2)')->text;
say $phone;
my $fax = $dom->at('div.phone > p:nth-of-type(4)')->text;
say $fax;
[download]

Prints:

0123-4 56 78 90
just the fax ma'am
[download]

Let us know if you have any problems or your input data is somehow weirder.

Update: Sorry, late in the day on a Saturday here. Since the HTML isn't valid, and I'm guessing you can't change that try:

#!/usr/bin/perl
use strict;
use warnings;
use Mojo::DOM;
use Mojo::Util qw(trim);
use feature 'say';

my $html = '<div class="phone">
<div class="icon"></div>
<p class="title">Telephone</p>
<p>0123-4 56 78 90          
<p class="title">Telefax</p>
<p>just the fax ma\'am
</div>';

my $dom = Mojo::DOM->new( $html );
my $phone = trim( $dom->at('div.phone > p:nth-of-type(2)')->text );
say $phone;
my $fax = trim( $dom->at('div.phone > p:nth-of-type(4)')->text );
say $fax;
[download]

Which still prints:

0123-4 56 78 90
just the fax ma'am
[download]