I would try wrapping in {% raw %}{% endraw %} tags. (wrong)
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I should have read the question better: Mark was closer than I was. The Communication List block does not give us a communication object, but it does give us the Id of the communication (as Row.Id )

Using that Id we can write an entity command that grabs what we want like this:
{% communication id:'{{ Row.Id }}' %}
{{ communication.FromEmail }}
{% endcommunication %}
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{% to get the sms information as well: %}
{% assign info = '' %}
{% communication id:'{{ Row.Id }}' %}
{% assign email = communication.FromEmail %}
{% if email != empty %}
{% assign info = info | Append:email %}
{% endif %}
{% assign num = communication.SMSFromDefinedValue.Description %}
{% if num != empty %}
{% assign info = info | Append:num %}
{% endif %}
{% endcommunication %}
{{ info }}