Phoenix Ecto conditional where

The simplest thing you can do in this particular situation, is refactor the code a little to move out the expressions which you are doing in either branch of the code:

  def search(search_term) do
    wildcard_search = "%#{search_term}%"
    query = case Decimal.parse(search_term) do
      {amount_decimal, _} ->
        # Input is decimal
        from(ce in CashflowEntry,
          where: ce.amount == ^amount_decimal or ilike(ce.note, ^wildcard_search)
        )
      _ ->
        # Input is alphanumeric
        from(ce in CashflowEntry, where: ilike(ce.note, ^wildcard_search))
    end

  Repo.all(query)
  end

And at this point, you might as well move the case statement to a helper function:

  def search(search_term) do
  search_term
  |> search_query()
  |> Repo.all()
  end
  
  # You might consider making this function public to test it separately
  defp search_query(search_term) do
    wildcard_search = "%#{search_term}%"
    query = case Decimal.parse(search_term) do
      {amount_decimal, _} ->
        # Input is decimal
        from(ce in CashflowEntry,
          where: ce.amount == ^amount_decimal or ilike(ce.note, ^wildcard_search)
        )
      _ ->
        # Input is alphanumeric
        from(ce in CashflowEntry, where: ilike(ce.note, ^wildcard_search))
    end
  end

There is to my knowledge no simple possibility to move the check of whether the input is a string or a number into the query to turn this code into a single query. (At least not without writing a raw SQL fragment, which is usually not recommended).