Such inferences are neither deductive (which assumes application of a valid inference rule) nor inductive (which assumes a generalization from a pattern of cases). This type of inference is called abductive, or "inference to the best explanation", see abductive reasoning. "Clearly" indicates that the explanation inferred is the best available. According to Harman, who coined the term "The inference to the best explanation" corresponds approximately to what others have called "abduction," the method of hypothesis," "hypothetic inference," "the method of elimination," "eliminative induction," and theoretical inference". Some authors still call any non-deductive reasoning "inductive", but such use is a bit archaic.
The form of reasoning in the OP example is this: A explains B; B, therefore A. If we try to translate this into classical logic by reducing "explains" to "implies" this amounts to concluding A from A → B and B. This form is the fallacy of affirming the consequent, which is of course deductively invalid, "where there is smoke there is fire" is the proverbial example. Nonetheless, in everyday reasoning, and even in science, we often rely on such inferences and consider them plausible, indeed we would not be able to figure out anything of substance without them. While deductively invalid, in proper contexts they produce hypotheses which have a good chance of being true, and are therefore relied on in planning behavior and in scientific methodology. Of course, as any hypotheses they may be refuted by subsequent evidence. The notion of abduction was introduced by Peirce, he credits Aristotle as inspiration:
"It is necessary to recognize three radically different kinds of arguments which I signalized in 1867... I suppose that the three were given by Aristotle in the Prior Analytics... Aristotle, in that chapter on Abduction, was even in that case evidently groping for that mode of inference which I call by the otherwise quite useless name of Abduction -- a word which is only employed in logic to translate the "apagoge" of that chapter." [second Prior Analytics, chapter 25].
The three modes of inference, and abduction in particular, featured in Peirce's attempt to codify the "logic of science", see SEP's Deduction, Induction, and Abduction in Peirce:
"Prior to about 1865, thinkers on logic commonly had divided arguments into two subclasses: the class of deductive arguments (a.k.a. necessary inferences) and the class of inductive arguments (a.k.a. probable inferences)... The most important extension Peirce made of his earliest views on what deduction, induction, and abduction involved was to integrate the three argument forms into his view of the systematic procedure for seeking truth that he called the “scientific method.”
Scientific method begins with abduction or hypothesis: because of some perhaps surprising or puzzling phenomenon, a conjecture or hypothesis is made about what actually is going on. This hypothesis should be such as to explain the surprising phenomenon, such as to render the phenomenon more or less a matter of course if the hypothesis should be true. Scientific method then proceeds to the stage of deduction: by means of necessary inferences, conclusions are drawn from the provisionally-adopted hypothesis about the obtaining of phenomena other than the surprising one that originally gave rise to the hypothesis. Conclusions are reached, that is to say, about other phenomena that must obtain if the hypothesis should actually be true. These other phenomena must be such that experimental tests can be performed whose results tell us whether the further phenomena do obtain or do not obtain. Finally, scientific method proceeds to the stage of induction: experiments are actually carried out in order to test the provisionally-adopted hypothesis by ascertaining whether the deduced results do or do not obtain."
It should be clear now that reading "A explains B" as merely "A implies B" is insufficient, the relation of implication is too weak, and may be accidental. It turned out surprisingly difficult to state precisely what "explains" amounts to beyond that, usually it is expected that it fall under some unifying account of phenomena, see Theories of Explanation. Even so, more than one explanation may be possible and abduction must select among them based on additional criteria, hence inference to the "best" explanation.
